What is ((x-3))/((x-4))+((x-4))/((x+3)) ?

The solution to ((x-3))/((x-4))+((x-4))/((x+3)) is (2x^2-8x+7)/((x-4)(x+3))

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simplify ((x-3))/((x-4))+((x-4))/((x+3))

simplify

\frac{( x - 3 )}{( x - 4 )} + \frac{( x - 4 )}{( x + 3 )}

\frac{2 x ^{2} - 8 x + 7}{( x - 4 ) ( x + 3 )}

Solution steps

\frac{x - 3}{x - 4} + \frac{x - 4}{x + 3}

Least Common Multiplier of

x - 4, x + 3 : (x - 4) (x + 3)

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

(x - 3) (x + 3) + (x - 4)^{2} : 2 x^{2} - 8 x + 7

= \frac{2 x ^{2} - 8 x + 7}{( x - 4 ) ( x + 3 )}

y^{9} - y^{10}

(n^{0})^{4}

(\frac{x + 1}{x})^{6}

2 x + 7 x - 15

(2 n - m)^{3}

What is ((x-3))/((x-4))+((x-4))/((x+3)) ?
The solution to ((x-3))/((x-4))+((x-4))/((x+3)) is (2x^2-8x+7)/((x-4)(x+3))