# DIVIDING RATIONAL EXPRESSIONS

The following steps would be useful to understand how to divide a rational expression by another rational expression.

Step 1 :

Write the first rational expression as it is. Change the division to multiplication and take reciprocal of the second rational expression.

Step 2 :

Factor both numerator and denominator, if possible.

Step 3 :

Identify the common factor at both numerator and denominator.

Step 4 :

The common factor identified at both numerator and denominator should be multiplied by the other terms.

Step 5 :

Now, get rid of the common factor at both numerator and denominator.

Example 1 :

Simplify :

Solution :

2a+ 5a + 3 =  (a + 1)(2a + 3)

2a+ 7a + 6 = (2a + 3)(a + 2)

a+ 6a + 5 = (a + 1)(a + 5)

-5a- 35a - 50 = -5(a2 + 7a + 10) = -5(a + 2)(a + 5)

Example 2 :

Simplify :

Solution :

b2 + 3b - 28 = (b - 4)(b + 7)

b2 + 4b + 4 = (b + 2)(b + 2)

b2 - 49 = b2 - 72 = (b - 7)(b + 7)

b2 - 5b - 14 = (b - 7)(b + 2)

Example 3 :

Simplify :

Solution :

Example 4 :

Simplify :

Solution :

12t2 - 22t + 8 = 2(6t2 - 11t + 4) = 2(3t - 4)(2t - 1)

3t2 + 2t - 8 = (t + 2)(3t - 4)

2t+ 4t = 2t(t + 2)

Example 5 :

Find the value of x2y-2.

Solution :

Example 6 :

If a polynomial p(x) = x2 - 5x - 14 is divided by another polynomial q(x), we get (x - 7)/(x + 2). Find q (x).

Solution :

Take reciprocal on both sides.

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