# What is the first step to perform when multiplying or dividing rational expressions to express them in their simplest form? How does

What is the first step to perform when multiplying or dividing rational expressions to express them in their simplest form? How does this step help in reducing the expression to its simplest form?

## This Post Has 3 Comments

1. ryliepeloquinf says:

$\frac{2(x-1)(2x+9)}{(x-3)(x-2)}$

Step-by-step explanation:

$\frac{4x}{(x-3)}+\frac{6}{(x+2)}$

= $\frac{4x(x+2)}{(x-3)(x+2)}+\frac{6(x-3)}{(x+2)(x-3)}$

Now we have done the denominators of each term of the expression equal.

$\frac{4x(x+2)}{(x-3)(x+2)}+\frac{6(x-3)}{(x+2)(x-3)}$

= $\frac{4x(x+2)+6(x-3)}{(x-3)(x+2)}$

= $\frac{4x^{2}+8x+6x-18}{(x-3)(x+2)}$

= $\frac{4x^{2}+14x-18}{(x-3)(x-2)}$

Now factorize the numerator of the fraction.

4x² + 14x - 18 = 2(2x² + 7x - 9)

= 2(2x² + 9x - 2x - 9)

= 2[x(2x + 9) - 1(2x + 9)]

= 2(x - 1)(2x + 9)

Therefore, $\frac{2(x-1)(2x+9)}{(x-3)(x-2)}$ will be the answer.

2. belindajolete says:

After adding or subtracting two rational expressions, you should put the result in simplest form by reducing it.

3. terrell31 says:

It’s pp