What is (x+3)/(x^2-6x+9)-(x+2)/(x^2-9)-5/(3-x) ?

The solution to (x+3)/(x^2-6x+9)-(x+2)/(x^2-9)-5/(3-x) is (5x^2+7x-30)/((x-3)^2(x+3))

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simplify (x+3)/(x^2-6x+9)-(x+2)/(x^2-9)-5/(3-x)

simplify

\frac{x + 3}{x ^{2} - 6 x + 9} - \frac{x + 2}{x ^{2} - 9} - \frac{5}{3 - x}

\frac{5 x ^{2} + 7 x - 30}{( x - 3 ) ^{2} ( x + 3 )}

Solution steps

\frac{x + 3}{x ^{2} - 6 x + 9} - \frac{x + 2}{x ^{2} - 9} - \frac{5}{3 - x}

Least Common Multiplier of

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

Adjust Fractions based on the LCM

= \frac{- ( x - 3 ) ( x + 3 ) ^{2}}{( x - 3 ) ^{2} ( x + 3 ) ( - x + 3 )} - \frac{( x + 2 ) ( - x ^{2} + 6 x - 9 )}{( x - 3 ) ^{2} ( x + 3 ) ( - x + 3 )} - \frac{- 5 ( x - 3 ) ( x + 3 ) ( - x + 3 )}{( x - 3 ) ^{2} ( x + 3 ) ( - x + 3 )}

Apply the fraction rule:

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

= \frac{- ( x - 3 ) ( x + 3 ) ^{2} - ( x + 2 ) ( - x ^{2} + 6 x - 9 ) - ( - 5 ( x - 3 ) ( x + 3 ) ( - x + 3 ) )}{( x - 3 ) ^{2} ( x + 3 ) ( - x + 3 )}

Simplify

- (x - 3) (x + 3)^{2} - (x + 2) (- x^{2} + 6 x - 9) - (- 5 (x - 3) (x + 3) (- x + 3)) : - (x - 3) (x + 3)^{2} - (x + 2) (- x^{2} + 6 x - 9) - 5 (x - 3)^{2} (x + 3)

= \frac{- ( x - 3 ) ( x + 3 ) ^{2} - ( x + 2 ) ( - x ^{2} + 6 x - 9 ) - 5 ( x - 3 ) ^{2} ( x + 3 )}{( x - 3 ) ^{2} ( x + 3 ) ( - x + 3 )}

Simplify

- (x - 3) (x + 3)^{2} - (x + 2) (- x^{2} + 6 x - 9) - 5 (x - 3)^{2} (x + 3) : - 5 x^{3} + 8 x^{2} + 51 x - 90

= \frac{- 5 x ^{3} + 8 x ^{2} + 51 x - 90}{( x - 3 ) ^{2} ( x + 3 ) ( - x + 3 )}

Cancel

\frac{- 5 x ^{3} + 8 x ^{2} + 51 x - 90}{( x - 3 ) ^{2} ( x + 3 ) ( - x + 3 )} : \frac{5 x ^{2} + 7 x - 30}{( x - 3 ) ^{2} ( x + 3 )}

= \frac{5 x ^{2} + 7 x - 30}{( x - 3 ) ^{2} ( x + 3 )}

(\frac{2 ^{m}}{2 ^{- 3}})^{2}

sec (θ) cos (θ)

(1 - cos (2 x))^{2}

sin^{4} (θ) - cos^{4} (θ)

x^{2} + 15 x + 14

What is (x+3)/(x^2-6x+9)-(x+2)/(x^2-9)-5/(3-x) ?
The solution to (x+3)/(x^2-6x+9)-(x+2)/(x^2-9)-5/(3-x) is (5x^2+7x-30)/((x-3)^2(x+3))