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

The solution to expand (3x+1)/(x^2-9)-2/(x+3) is (x+7)/(x^2-9)

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expand (3x+1)/(x^2-9)-2/(x+3)

expand

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

\frac{x + 7}{x ^{2} - 9}

Solution steps

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

Factor

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

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

Least Common Multiplier of

(x + 3) (x - 3), x + 3 : (x + 3) (x - 3)

Adjust Fractions based on the LCM

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

Since the denominators are equal, combine the fractions:

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

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

Expand

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

= \frac{3 x + 1 - 2 ( x - 3 )}{x ^{2} - 9}

Expand

3 x + 1 - 2 (x - 3) : x + 7

= \frac{x + 7}{x ^{2} - 9}

- \frac{0.1 ( 2 s + 5 )}{s + 1}

(1 + 2 x - 3 x^{2})^{6}

e^{2 x} (e^{x} - e^{- x})

e^{t} U (t - 3)

\frac{( 3 s + 1 )}{( s + 8 ) ( s + 1 ) ( s + 6 )}

What is expand (3x+1)/(x^2-9)-2/(x+3) ?
The solution to expand (3x+1)/(x^2-9)-2/(x+3) is (x+7)/(x^2-9)