What is (x+3)/(x^2-25)-(x-1)/(x-5)+3/(x+3) ?

The solution to (x+3)/(x^2-25)-(x-1)/(x-5)+3/(x+3) is (-x^3-3x^2-x-51)/((x+5)(x-5)(x+3))

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simplify (x+3)/(x^2-25)-(x-1)/(x-5)+3/(x+3)

simplify

\frac{x + 3}{x ^{2} - 25} - \frac{x - 1}{x - 5} + \frac{3}{x + 3}

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

Solution steps

\frac{x + 3}{x ^{2} - 25} - \frac{x - 1}{x - 5} + \frac{3}{x + 3}

Least Common Multiplier of

x^{2} - 25, x - 5, x + 3 : (x + 5) (x - 5) (x + 3)

Adjust Fractions based on the LCM

= \frac{( x + 3 ) ^{2}}{( x + 5 ) ( x - 5 ) ( x + 3 )} - \frac{( x - 1 ) ( x + 5 ) ( x + 3 )}{( x + 5 ) ( x - 5 ) ( x + 3 )} + \frac{3 ( x + 5 ) ( x - 5 )}{( x + 5 ) ( x - 5 ) ( x + 3 )}

Apply the fraction rule:

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

= \frac{( x + 3 ) ^{2} - ( x - 1 ) ( x + 5 ) ( x + 3 ) + 3 ( x + 5 ) ( x - 5 )}{( x + 5 ) ( x - 5 ) ( x + 3 )}

Simplify

(x + 3)^{2} - (x - 1) (x + 5) (x + 3) + 3 (x + 5) (x - 5) : - x^{3} - 3 x^{2} - x - 51

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

- \frac{2}{3} - \frac{4}{7} + \frac{5}{3} + 3

\frac{lo g _{10} ( 4 )}{lo g _{10} ( 2 )}

(- 8)^{4}

- 3 (x + h)^{2}

\frac{x + 2}{2 x ^{2} + 13 x + 20} - \frac{x + 3}{2 x ^{2} + 13 x + 20}

What is (x+3)/(x^2-25)-(x-1)/(x-5)+3/(x+3) ?
The solution to (x+3)/(x^2-25)-(x-1)/(x-5)+3/(x+3) is (-x^3-3x^2-x-51)/((x+5)(x-5)(x+3))