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Chapter 8: Q 237 (page 954)

Add4mm2+6m-7+2m2+10m+21.

Short Answer

Expert verified

The sum is2(2m2+7m-1)(m+7)(m-1)(m+3).

Step by step solution

01

Given Information      

The Given expression is4mm2+6m-7+2m2+10m+21.

02

Find the LCD of denominators.  

Factor the denominators.

m2+6m-7=(m+7)(m-1)

m2+10m+21=(m+7)(m+3)

LCD=(m+7)(m-1)(m+3)

Rewrite the expression in factored form.

=4m(m+7)(m-1)+2(m+7)(m+3)

03

Rewrite each fraction as an equivalent fraction with the LCD.      

=4m(m+3)(m+7)(m-1)(m+3)+2(m-1)(m+7)(m-1)(m+3)=4m2+12m(m+7)(m-1)(m+3)+2m-2(m+7)(m-1)(m+3)

04

Add

Take common denominator

=4m2+12m+2m-2(m+7)(m-1)(m+3)

Simplify numerator.

=4m2+14m-2(m+7)(m-1)(m+3)

role="math" localid="1648377969244" =2(2m2+7m-1)(m+7)(m-1)(m+3)

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