** **A rational expression is a polynomial term, in the form of fraction. It may be any type of polynomial such as monomial, trinomial and binomial. Multiplication of rational expression is same as normal multiplication of fractions. A rational expression has a polynomial in both numerator or only in denominator.

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Below are the steps to multiply rational expressions.

**Step 1:** First do the multiplication of numerators of the rational expressions. If possible, factor the obtained result.

**Step 2:** Do the multiplication of denominators of rational expression and if possible factor the resultant value.

**Step 3:** Now, write the result by writing fraction which has above two answers. The final answer is again simplified if possible.

Let us see an example on how to multiply and simplify rational expressions.

Let us multiply and simplify rational expressions $\frac{8x}{x^2 + 14x + 49}$ x $\frac{x^2 + 2x - 35}{12x^6}$

Given rational expressions are, $\frac{8x}{x^2 + 14x + 49}$ x $\frac{x^2 + 2x - 35}{12x^6}$**Step 1:**

The factor of a first rational expression is,

$\frac{8x}{x^2 + 14x + 49}$ = $\frac{8x}{(x + 7)(x + 7)}$**Step 2:**

The factors of second rational expression is,

$\frac{x^2 + 2x - 35}{12x^6}$ = $\frac{(x + 7)(x - 5)}{12x^6}$**Step 3:**

Now, the multiplication of rational expressions is,

$\frac{8x}{(x + 7)(x + 7)}$ x $\frac{(x + 7)(x - 5)}{12x^6}$

The common factor in both rational expression is (x + 7) and x.

$\frac{8x}{(x + 7)(x + 7)}$ x $\frac{(x + 7)(x - 5)}{12x^6}$ = $\frac{8}{x + 7}$ x $\frac{(x - 5)}{12x^5}$

= $\frac{8(x - 5)}{(x + 7)(12x^5)}$

We can also cancel the numbers 8 and 12 by 4.

$\frac{8(x - 5)}{(x + 7)(12x^5)}$ = $\frac{2(x - 5)}{(x + 7)(3x^5)}$

Given expressions are $\frac{6x^5}{x^2+16x+63}$ and $\frac{x^2+4x-21}{9x^4}$**Step 1: **Simplify first expression, $\frac{6x^5}{x^2+16x+63}$

= $\frac{6x^5}{(x + 9)(x + 7)}$

Step 2:

= $\frac{(x + 7)(x - 3)}{9x^4}$

Step 3:

$\frac{6x^5}{(x + 9)(x + 7)}$ * $\frac{(x + 7)(x - 3)}{9x^4}$ = $\frac{2x(x - 3)}{3(x + 9)}$

Given expressions are $\frac{12x^6}{x^2+15x+36}$ and $\frac{x^2+10x-24}{3x^5}$**Step 1: **Simplify first expression, $\frac{12x^6}{x^2+15x+36}$

= $\frac{12x^6}{(x+12)(x + 3)}$

= $\frac{(x + 12)(x - 2)}{3x^5}$

Step 3:

$\frac{12x^6}{(x+12)(x + 3)}$ * $\frac{(x + 12)(x - 2)}{3x^5}$

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

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

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