What is (2x)/(x^2-9)-1/(x-3) ?

The solution to (2x)/(x^2-9)-1/(x-3) is 1/(x+3)

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simplify (2x)/(x^2-9)-1/(x-3)

simplify

\frac{2 x}{x ^{2} - 9} - \frac{1}{x - 3}

\frac{1}{x + 3}

Solution steps

\frac{2 x}{x ^{2} - 9} - \frac{1}{x - 3}

Least Common Multiplier of

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

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

2 x - (x + 3) : x - 3

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

Cancel the common factor:

x - 3

= \frac{1}{x + 3}

1 \times 2 \times 3 \times 4 \times 5

35 - 220

55 + 25

\frac{1}{3} \cdot (- 6)

\frac{1}{3} \cdot (- 5)