What is 9/(x^2-12x+36)+x/(x^2-36) ?

The solution to 9/(x^2-12x+36)+x/(x^2-36) is (x^2+3x+54)/((x-6)^2(x+6))

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simplify 9/(x^2-12x+36)+x/(x^2-36)

simplify

\frac{9}{x ^{2} - 12 x + 36} + \frac{x}{x ^{2} - 36}

\frac{x ^{2} + 3 x + 54}{( x - 6 ) ^{2} ( x + 6 )}

Solution steps

\frac{9}{x ^{2} - 12 x + 36} + \frac{x}{x ^{2} - 36}

Least Common Multiplier of

x^{2} - 12 x + 36, x^{2} - 36 : (x - 6)^{2} (x + 6)

Adjust Fractions based on the LCM

= \frac{9 ( x + 6 )}{( x - 6 ) ^{2} ( x + 6 )} + \frac{x ( x - 6 )}{( x - 6 ) ^{2} ( x + 6 )}

Apply the fraction rule:

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

= \frac{9 ( x + 6 ) + x ( x - 6 )}{( x - 6 ) ^{2} ( x + 6 )}

Simplify

9 (x + 6) + x (x - 6) : x^{2} + 3 x + 54

= \frac{x ^{2} + 3 x + 54}{( x - 6 ) ^{2} ( x + 6 )}

125 a^{3} + 1

\frac{d - 2}{d ^{2} - 4} + \frac{4}{d ^{2} + 4 d + 4}

\frac{\frac{1}{x ^{2}}}{\frac{1}{x}}

\frac{50 5}{4}

\frac{3 ^{9}}{3 ^{- 5}}

What is 9/(x^2-12x+36)+x/(x^2-36) ?
The solution to 9/(x^2-12x+36)+x/(x^2-36) is (x^2+3x+54)/((x-6)^2(x+6))