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Chapter 8: Q 250 (page 955)

Simplify2qq+5+3q-3-13q+15q2+2q-15.

Short Answer

Expert verified

The result is2q2-16q(q+5)(q-3).

Step by step solution

01

Given Information      

The Given expression is2qq+5+3q-3-13q+15q2+2q-15.

02

Find the LCD of denominators.   

Factor the denominators.

q2+2q-15=(q+5)(q-3)

Rewrite the expression in factored form.

=2qq+5+3q-3-13q+15(q+5)(q-3)

03

Rewrite each fraction as an equivalent fraction with the LCD.  

=2q(q-3)(q+5)(q-3)+3(q+5)(q+5)(q-3)-13q+15(q+5)(q-3)=2q2-6q(q+5)(q-3)+3q+15(q+5)(q-3)-13q+15(q+5)(q-3)

04

Simplify. 

Take common denominator.

=2q2-6q+3q+15-(13q+15)(q+5)(q-3)=2q2-3q+15-13q-15(q+5)(q-3)=2q2-16q(q+5)(q-3)

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