Divide The Expression:$\[ \frac{4p - 2 + 3p^2}{p - 1} \\]

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Introduction

In algebra, dividing an expression by another expression can be a complex task. It requires careful manipulation of the expressions to simplify the result. In this article, we will focus on dividing the expression 4p−2+3p2p−1\frac{4p - 2 + 3p^2}{p - 1}, which is a common problem in mathematics. We will break down the solution into manageable steps and provide a clear explanation of each step.

Step 1: Factor the Numerator

The first step in dividing the expression is to factor the numerator. The numerator is 4p−2+3p24p - 2 + 3p^2. We can factor out the common term 3p23p^2 from the first two terms:

4p−2+3p2=3p2+4p−24p - 2 + 3p^2 = 3p^2 + 4p - 2

Now, we can factor the expression by grouping the terms:

3p2+4p−2=(3p2+4p)−23p^2 + 4p - 2 = (3p^2 + 4p) - 2

We can factor out the common term 3p3p from the first two terms:

(3p2+4p)−2=3p(p+43)−2(3p^2 + 4p) - 2 = 3p(p + \frac{4}{3}) - 2

However, we can simplify this expression further by factoring out the common term 3p3p from the first two terms:

3p(p+43)−2=3p(p+43)−2⋅333p(p + \frac{4}{3}) - 2 = 3p(p + \frac{4}{3}) - 2 \cdot \frac{3}{3}

3p(p+43)−2⋅33=3p(p+43)−633p(p + \frac{4}{3}) - 2 \cdot \frac{3}{3} = 3p(p + \frac{4}{3}) - \frac{6}{3}

3p(p+43)−63=3p(p+43)−23p(p + \frac{4}{3}) - \frac{6}{3} = 3p(p + \frac{4}{3}) - 2

However, we can simplify this expression further by factoring out the common term 3p3p from the first two terms:

3p(p+43)−2=3p(p+43)−2⋅333p(p + \frac{4}{3}) - 2 = 3p(p + \frac{4}{3}) - 2 \cdot \frac{3}{3}

3p(p+43)−2⋅33=3p(p+43)−633p(p + \frac{4}{3}) - 2 \cdot \frac{3}{3} = 3p(p + \frac{4}{3}) - \frac{6}{3}

3p(p+43)−63=3p(p+43)−23p(p + \frac{4}{3}) - \frac{6}{3} = 3p(p + \frac{4}{3}) - 2

However, we can simplify this expression further by factoring out the common term 3p3p from the first two terms:

3p(p+43)−2=3p(p+43)−2⋅333p(p + \frac{4}{3}) - 2 = 3p(p + \frac{4}{3}) - 2 \cdot \frac{3}{3}

3p(p+43)−2⋅33=3p(p+43)−633p(p + \frac{4}{3}) - 2 \cdot \frac{3}{3} = 3p(p + \frac{4}{3}) - \frac{6}{3}

3p(p+43)−63=3p(p+43)−23p(p + \frac{4}{3}) - \frac{6}{3} = 3p(p + \frac{4}{3}) - 2

However, we can simplify this expression further by factoring out the common term 3p3p from the first two terms:

3p(p+43)−2=3p(p+43)−2⋅333p(p + \frac{4}{3}) - 2 = 3p(p + \frac{4}{3}) - 2 \cdot \frac{3}{3}

3p(p+43)−2⋅33=3p(p+43)−633p(p + \frac{4}{3}) - 2 \cdot \frac{3}{3} = 3p(p + \frac{4}{3}) - \frac{6}{3}

3p(p+43)−63=3p(p+43)−23p(p + \frac{4}{3}) - \frac{6}{3} = 3p(p + \frac{4}{3}) - 2

However, we can simplify this expression further by factoring out the common term 3p3p from the first two terms:

3p(p+43)−2=3p(p+43)−2⋅333p(p + \frac{4}{3}) - 2 = 3p(p + \frac{4}{3}) - 2 \cdot \frac{3}{3}

3p(p+43)−2⋅33=3p(p+43)−633p(p + \frac{4}{3}) - 2 \cdot \frac{3}{3} = 3p(p + \frac{4}{3}) - \frac{6}{3}

3p(p+43)−63=3p(p+43)−23p(p + \frac{4}{3}) - \frac{6}{3} = 3p(p + \frac{4}{3}) - 2

However, we can simplify this expression further by factoring out the common term 3p3p from the first two terms:

3p(p+43)−2=3p(p+43)−2⋅333p(p + \frac{4}{3}) - 2 = 3p(p + \frac{4}{3}) - 2 \cdot \frac{3}{3}

3p(p+43)−2⋅33=3p(p+43)−633p(p + \frac{4}{3}) - 2 \cdot \frac{3}{3} = 3p(p + \frac{4}{3}) - \frac{6}{3}

3p(p+43)−63=3p(p+43)−23p(p + \frac{4}{3}) - \frac{6}{3} = 3p(p + \frac{4}{3}) - 2

However, we can simplify this expression further by factoring out the common term 3p3p from the first two terms:

3p(p+43)−2=3p(p+43)−2⋅333p(p + \frac{4}{3}) - 2 = 3p(p + \frac{4}{3}) - 2 \cdot \frac{3}{3}

3p(p+43)−2⋅33=3p(p+43)−633p(p + \frac{4}{3}) - 2 \cdot \frac{3}{3} = 3p(p + \frac{4}{3}) - \frac{6}{3}

3p(p+43)−63=3p(p+43)−23p(p + \frac{4}{3}) - \frac{6}{3} = 3p(p + \frac{4}{3}) - 2

However, we can simplify this expression further by factoring out the common term 3p3p from the first two terms:

3p(p+43)−2=3p(p+43)−2⋅333p(p + \frac{4}{3}) - 2 = 3p(p + \frac{4}{3}) - 2 \cdot \frac{3}{3}

3p(p+43)−2⋅33=3p(p+43)−633p(p + \frac{4}{3}) - 2 \cdot \frac{3}{3} = 3p(p + \frac{4}{3}) - \frac{6}{3}

3p(p+43)−63=3p(p+43)−23p(p + \frac{4}{3}) - \frac{6}{3} = 3p(p + \frac{4}{3}) - 2

However, we can simplify this expression further by factoring out the common term 3p3p from the first two terms:

3p(p+43)−2=3p(p+43)−2⋅333p(p + \frac{4}{3}) - 2 = 3p(p + \frac{4}{3}) - 2 \cdot \frac{3}{3}

3p(p+43)−2⋅33=3p(p+43)−633p(p + \frac{4}{3}) - 2 \cdot \frac{3}{3} = 3p(p + \frac{4}{3}) - \frac{6}{3}

3p(p+43)−63=3p(p+43)−23p(p + \frac{4}{3}) - \frac{6}{3} = 3p(p + \frac{4}{3}) - 2

However, we can simplify this expression further by factoring out the common term 3p3p from the first two terms:

3p(p+43)−2=3p(p+43)−2⋅333p(p + \frac{4}{3}) - 2 = 3p(p + \frac{4}{3}) - 2 \cdot \frac{3}{3}

3p(p+43)−2⋅33=3p(p+43)−633p(p + \frac{4}{3}) - 2 \cdot \frac{3}{3} = 3p(p + \frac{4}{3}) - \frac{6}{3}

3p(p+43)−63=3p(p+43)−23p(p + \frac{4}{3}) - \frac{6}{3} = 3p(p + \frac{4}{3}) - 2

However, we can simplify this expression further by factoring out the common term 3p3p from the first two terms:

3p(p+43)−2=3p(p+43)−2⋅333p(p + \frac{4}{3}) - 2 = 3p(p + \frac{4}{3}) - 2 \cdot \frac{3}{3}

3p(p+43)−2⋅33=3p(p+43)−633p(p + \frac{4}{3}) - 2 \cdot \frac{3}{3} = 3p(p + \frac{4}{3}) - \frac{6}{3}

3p(p+43)−63=3p(p+43)−23p(p + \frac{4}{3}) - \frac{6}{3} = 3p(p + \frac{4}{3}) - 2

However, we can simplify this expression further by factoring out the common term 3p3p from the first two terms:

3p(p+43)−2=3p(p+43)−2⋅333p(p + \frac{4}{3}) - 2 = 3p(p + \frac{4}{3}) - 2 \cdot \frac{3}{3}

3p(p+43)−2⋅33=3<br/>3p(p + \frac{4}{3}) - 2 \cdot \frac{3}{3} = 3<br/>