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

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

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

simplify

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

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

Solution steps

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

Least Common Multiplier of

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

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

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

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

7 + \frac{3}{2}

\frac{20}{32}

\frac{1}{2 + 4 i}

\frac{75}{40}

x^{5^{2}}

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