How do you do 5//2x-1 + 6x+7// 1-4x^2 ?

Question

Adding and Subtracting Expressions with Different Denominators.

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Answer 1 · 2018-06-02T17:18:01

$=(24x^2+4x+22)/(4x^2-1)$

$5/(2x-1)+6x+7/(1-4x^2)=5/(2x-1)+6x-7/((1-2x)(1+2x))$
$=5/(2x-1)+6x+7/((2x-1)(2x+1))$

The lcm is $(2x+1)(2x-1)$

$=(5(2x+1)+6x(2x-1)(2x+1)+7(1))/((2x-1)(2x+1))$

$=(10x+15+6x(4x^2-1)+7)/(4x^2-1)$

$(=10x+15+24x^2-6x+7)/(4x^2-1)$

$=(24x^2+4x+22)/(4x^2-1)$