6. $\frac{a}{x} +\frac{b}{y} = 1$ Rearrange That Formula So That The Subject Is: a) $x$ b) $y$ c) $a$ d) $b$ Answer Question A, B, C, And D. And The Formula Is Given. ⬆️

Rearranging the Formula: 6. $\frac{a}{x} +\frac{b}{y} = 1$

In this article, we will explore the process of rearranging the given formula, $\frac{a}{x} +\frac{b}{y} = 1$, to isolate the subject variable. The subject variable is the variable that we want to solve for in the equation. We will rearrange the formula to isolate the subject variable for each of the variables: $x$, $y$, $a$, and $b$.

Rearranging the Formula to Isolate $x$

To isolate $x$, we need to get rid of the terms that contain $x$ in the denominator. We can do this by multiplying both sides of the equation by $xy$, which is the least common multiple of the denominators.

$$\frac{a}{x} +\frac{b}{y} = 1$$

$$\frac{a}{x} \cdot xy +\frac{b}{y} \cdot xy = 1 \cdot xy$$

$$ay + bx = xy$$

Now, we can subtract $bx$ from both sides of the equation to get:

$$ay = xy - bx$$

Next, we can subtract $xy$ from both sides of the equation to get:

$$ay - xy = -bx$$

Finally, we can factor out $y$ from the left-hand side of the equation to get:

$$y(a - x) = -bx$$

Now, we can divide both sides of the equation by $y(a - x)$ to get:

$$x = \frac{-bx}{y(a - x)}$$

However, we can simplify this expression further by multiplying both the numerator and denominator by $-1$:

$$x = \frac{bx}{-y(a - x)}$$

$$x = \frac{bx}{y(a - x)}$$

This is the final expression for $x$.

Rearranging the Formula to Isolate $y$

To isolate $y$, we need to get rid of the terms that contain $y$ in the denominator. We can do this by multiplying both sides of the equation by $xy$, which is the least common multiple of the denominators.

$$\frac{a}{x} +\frac{b}{y} = 1$$

$$\frac{a}{x} \cdot xy +\frac{b}{y} \cdot xy = 1 \cdot xy$$

$$ay + bx = xy$$

Now, we can subtract $bx$ from both sides of the equation to get:

$$ay = xy - bx$$

Next, we can subtract $xy$ from both sides of the equation to get:

$$ay - xy = -bx$$

Finally, we can factor out $y$ from the left-hand side of the equation to get:

$$y(a - x) = -bx$$

Now, we can divide both sides of the equation by $a - x$ to get:

$$y = \frac{-bx}{a - x}$$

This is the final expression for $y$.

Rearranging the Formula to Isolate $a$

To isolate $a$, we need to get rid of the terms that contain $a$ in the numerator. We can do this by multiplying both sides of the equation by $x$, which is the denominator of the first term.

$$\frac{a}{x} +\frac{b}{y} = 1$$

$$\frac{a}{x} \cdot x +\frac{b}{y} \cdot x = 1 \cdot x$$

$$a +\frac{b}{y} \cdot x = x$$

Now, we can subtract $x$ from both sides of the equation to get:

$$a = x -\frac{b}{y} \cdot x$$

Next, we can factor out $x$ from the right-hand side of the equation to get:

$$a = x(1 -\frac{b}{y})$$

This is the final expression for $a$.

Rearranging the Formula to Isolate $b$

To isolate $b$, we need to get rid of the terms that contain $b$ in the numerator. We can do this by multiplying both sides of the equation by $y$, which is the denominator of the second term.

$$\frac{a}{x} +\frac{b}{y} = 1$$

$$\frac{a}{x} \cdot y +\frac{b}{y} \cdot y = 1 \cdot y$$

$$\frac{ay}{x} + b = y$$

Now, we can subtract $y$ from both sides of the equation to get:

$$\frac{ay}{x} = y - b$$

Next, we can subtract $y$ from both sides of the equation to get:

$$\frac{ay}{x} - y = -b$$

Finally, we can factor out $y$ from the left-hand side of the equation to get:

$$y(\frac{a}{x} - 1) = -b$$

Now, we can divide both sides of the equation by $y(\frac{a}{x} - 1)$ to get:

$$b = -\frac{y(\frac{a}{x} - 1)}{1}$$

However, we can simplify this expression further by multiplying both the numerator and denominator by $-1$:

$$b = \frac{y(\frac{a}{x} - 1)}{-1}$$

$$b = -y(\frac{a}{x} - 1)$$

This is the final expression for $b$.

In this article, we have rearranged the given formula, $\frac{a}{x} +\frac{b}{y} = 1$, to isolate the subject variable for each of the variables: $x$, $y$, $a$, and $b$. We have shown that the final expressions for $x$, $y$, $a$, and $b$ are:

• $x = \frac{bx}{y(a - x)}$
• $y = \frac{-bx}{a - x}$
• $a = x(1 -\frac{b}{y})$
• $b = -y(\frac{a}{x} - 1)$

These expressions can be used to solve for the subject variable in the given formula.
Q&A: Rearranging the Formula 6. $\frac{a}{x} +\frac{b}{y} = 1$

In our previous article, we explored the process of rearranging the given formula, $\frac{a}{x} +\frac{b}{y} = 1$, to isolate the subject variable for each of the variables: $x$, $y$, $a$, and $b$. In this article, we will answer some common questions related to rearranging this formula.

Q: What is the least common multiple (LCM) of the denominators?

A: The LCM of the denominators is the smallest number that both denominators can divide into evenly. In this case, the LCM of $x$ and $y$ is $xy$.

Q: Why do we multiply both sides of the equation by the LCM?

A: We multiply both sides of the equation by the LCM to get rid of the terms that contain the subject variable in the denominator. This allows us to isolate the subject variable and solve for it.

Q: How do we isolate the subject variable in the equation?

A: To isolate the subject variable, we need to get rid of the terms that contain the subject variable in the denominator. We can do this by multiplying both sides of the equation by the LCM, which is the least common multiple of the denominators.

Q: What is the final expression for $x$?

A: The final expression for $x$ is:

$$x = \frac{bx}{y(a - x)}$$

Q: What is the final expression for $y$?

A: The final expression for $y$ is:

$$y = \frac{-bx}{a - x}$$

Q: What is the final expression for $a$?

A: The final expression for $a$ is:

$$a = x(1 -\frac{b}{y})$$

Q: What is the final expression for $b$?

A: The final expression for $b$ is:

$$b = -y(\frac{a}{x} - 1)$$

Q: Can I use these expressions to solve for the subject variable in the given formula?

A: Yes, you can use these expressions to solve for the subject variable in the given formula. Simply plug in the values of the variables and solve for the subject variable.

Q: What if I have a different formula with different variables? Can I still use these expressions?

A: No, you cannot use these expressions for a different formula with different variables. The expressions we derived are specific to the given formula and variables. You will need to derive new expressions for a different formula.

In this article, we have answered some common questions related to rearranging the formula $\frac{a}{x} +\frac{b}{y} = 1$. We have shown that the final expressions for $x$, $y$, $a$, and $b$ are:

• $x = \frac{bx}{y(a - x)}$
• $y = \frac{-bx}{a - x}$
• $a = x(1 -\frac{b}{y})$
• $b = -y(\frac{a}{x} - 1)$

These expressions can be used to solve for the subject variable in the given formula.