What is 3/(4x^2)+x/(x^2-7) ?

The solution to 3/(4x^2)+x/(x^2-7) is (3x^2-21+4x^3)/(4x^2(x^2-7))

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simplify 3/(4x^2)+x/(x^2-7)

simplify

\frac{3}{4 x ^{2}} + \frac{x}{x ^{2} - 7}

\frac{3 x ^{2} - 21 + 4 x ^{3}}{4 x ^{2} ( x ^{2} - 7 )}

Solution steps

\frac{3}{4 x ^{2}} + \frac{x}{x ^{2} - 7}

Least Common Multiplier of

4 x^{2}, x^{2} - 7 : 4 x^{2} (x + 7) (x - 7)

Adjust Fractions based on the LCM

= \frac{3 ( x + 7 ) ( x - 7 )}{4 x ^{2} ( x + 7 ) ( x - 7 )} + \frac{4 x ^{3}}{4 x ^{2} ( x + 7 ) ( x - 7 )}

Apply the fraction rule:

\frac{a}{c} + \frac{b}{c} = \frac{a + b}{c}

= \frac{3 ( x + 7 ) ( x - 7 ) + 4 x ^{3}}{4 x ^{2} ( x + 7 ) ( x - 7 )}

Simplify

3 (x + 7) (x - 7) + 4 x^{3} : 3 x^{2} - 21 + 4 x^{3}

= \frac{3 x ^{2} - 21 + 4 x ^{3}}{4 x ^{2} ( x + 7 ) ( x - 7 )}

Apply Difference of Two Squares

(x + 7) (x - 7) : x^{2} - 7

= \frac{3 x ^{2} - 21 + 4 x ^{3}}{4 x ^{2} ( x ^{2} - 7 )}

w^{2} - 2 w + 1

16384

- (- \frac{1}{2})^{2}

\frac{( \frac{T}{p \cdot n ^{2} \cdot D ^{4}} )}{( \frac{x}{p \cdot n ^{3} \cdot D ^{5}} )}

\frac{1}{s ^{2} + s + 1 + \frac{1}{s + 1}}

What is 3/(4x^2)+x/(x^2-7) ?
The solution to 3/(4x^2)+x/(x^2-7) is (3x^2-21+4x^3)/(4x^2(x^2-7))