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

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

Adding and Subtracting Expressions with Different Denominators.

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Answer 1 · 2018-06-02T17:18:01

$= \frac{24 x^{2} + 4 x + 22}{4 x^{2} - 1}$ $=(24x^2+4x+22)/(4x^2-1)$

Explanation:

$\frac{5}{2 x - 1} + 6 x + \frac{7}{1 - 4 x^{2}} = \frac{5}{2 x - 1} + 6 x - \frac{7}{(1 - 2 x) (1 + 2 x)}$ $5/(2x-1)+6x+7/(1-4x^2)=5/(2x-1)+6x-7/((1-2x)(1+2x))$
$= \frac{5}{2 x - 1} + 6 x + \frac{7}{(2 x - 1) (2 x + 1)}$ $=5/(2x-1)+6x+7/((2x-1)(2x+1))$

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

$= \frac{5 (2 x + 1) + 6 x (2 x - 1) (2 x + 1) + 7 (1)}{(2 x - 1) (2 x + 1)}$ $=(5(2x+1)+6x(2x-1)(2x+1)+7(1))/((2x-1)(2x+1))$

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

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

$= \frac{24 x^{2} + 4 x + 22}{4 x^{2} - 1}$ $=(24x^2+4x+22)/(4x^2-1)$

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

Adding and Subtracting Expressions with Different Denominators.

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