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Chapter 8: Q 206 (page 954)

Add6q2-3q-10+5qq2-8q+15.

Short Answer

Expert verified

The sum is5q2+16q-18(q-3)(q-5)(q+2).

Step by step solution

01

Given Information 

The Given expression is6q2-3q-10+5qq2-8q+15.

02

Find the LCD of denominators. 

Factor the denominators.

q2-3q-10=(q+2)(q-5)

q2-8q+15=(q-3)(q-5)

LCD=(q-3)(q-5)(q+2)

Rewrite the expression in factored form.

=6(q+2)(q-5)+5q(q-3)(q-5)

03

Rewrite each fraction as an equivalent fraction with the LCD. 

=6(q-3)(q-3)(q-5)(q+2)+5q(q+2)(q-3)(q-5)(q+2)

=6q-18(q-3)(q-5)(q+2)+5q2+10q(q-3)(q-5)(q+2)

04

Add and simplify the numerator. 

Take common denominator.

=6q-18+5q2+10q(q-3)(q-5)(q+2)

=5q2+16q-18(q-3)(q-5)(q+2)

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