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

The solution to (4x+1)/(x^2-4)-3/(x-2) is (x-5)/((x+2)(x-2))

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simplify (4x+1)/(x^2-4)-3/(x-2)

simplify

\frac{4 x + 1}{x ^{2} - 4} - \frac{3}{x - 2}

\frac{x - 5}{( x + 2 ) ( x - 2 )}

Solution steps

\frac{4 x + 1}{x ^{2} - 4} - \frac{3}{x - 2}

Least Common Multiplier of

x^{2} - 4, x - 2 : (x + 2) (x - 2)

Adjust Fractions based on the LCM

= \frac{4 x + 1}{( x + 2 ) ( x - 2 )} - \frac{3 ( x + 2 )}{( x + 2 ) ( x - 2 )}

Apply the fraction rule:

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

= \frac{4 x + 1 - 3 ( x + 2 )}{( x + 2 ) ( x - 2 )}

Simplify

4 x + 1 - 3 (x + 2) : x - 5

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

(5 x^{2} - 2 x) + (6 x - 4)

65 - 25

1 - \frac{x}{1 + \frac{x}{\frac{1}{x - 1}}}

\frac{4}{5 + 1}

3 (x + 6) + 4 (2 x - 5)

What is (4x+1)/(x^2-4)-3/(x-2) ?
The solution to (4x+1)/(x^2-4)-3/(x-2) is (x-5)/((x+2)(x-2))