What is ((4r-1))/((9-r^2))+((4))/((r-3)) ?

The solution to ((4r-1))/((9-r^2))+((4))/((r-3)) is (13)/((r+3)(r-3))

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simplify ((4r-1))/((9-r^2))+((4))/((r-3))

simplify

\frac{( 4 r - 1 )}{( 9 - r ^{2} )} + \frac{( 4 )}{( r - 3 )}

\frac{13}{( r + 3 ) ( r - 3 )}

Solution steps

\frac{4 r - 1}{9 - r ^{2}} + \frac{4}{r - 3}

Least Common Multiplier of

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

Adjust Fractions based on the LCM

= \frac{- ( 4 r - 1 )}{( r + 3 ) ( r - 3 )} + \frac{4 ( r + 3 )}{( r + 3 ) ( r - 3 )}

Apply the fraction rule:

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

= \frac{- ( 4 r - 1 ) + 4 ( r + 3 )}{( r + 3 ) ( r - 3 )}

Simplify

- (4 r - 1) + 4 (r + 3) : 13

= \frac{13}{( r + 3 ) ( r - 3 )}

(6 - 2 x)^{3}

\frac{1}{cos ( x ) sin ( x )}

(47 - 11) (37 + 411)

\frac{sin ^{2} ( x )}{1 + cos ( x )}

(cos (x) + sin (x))^{2}

What is ((4r-1))/((9-r^2))+((4))/((r-3)) ?
The solution to ((4r-1))/((9-r^2))+((4))/((r-3)) is (13)/((r+3)(r-3))