What is 6/(2x+1)-x/(x+3) ?

The solution to 6/(2x+1)-x/(x+3) is (-2x^2+5x+18)/((x+3)(2x+1))

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simplify 6/(2x+1)-x/(x+3)

simplify

\frac{6}{2 x + 1} - \frac{x}{x + 3}

\frac{- 2 x ^{2} + 5 x + 18}{( x + 3 ) ( 2 x + 1 )}

Solution steps

\frac{6}{2 x + 1} - \frac{x}{x + 3}

Least Common Multiplier of

2 x + 1, x + 3 : (x + 3) (2 x + 1)

Adjust Fractions based on the LCM

= \frac{6 ( x + 3 )}{( x + 3 ) ( 2 x + 1 )} - \frac{x ( 2 x + 1 )}{( x + 3 ) ( 2 x + 1 )}

Apply the fraction rule:

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

= \frac{6 ( x + 3 ) - x ( 2 x + 1 )}{( x + 3 ) ( 2 x + 1 )}

Simplify

6 (x + 3) - x (2 x + 1) : - 2 x^{2} + 5 x + 18

= \frac{- 2 x ^{2} + 5 x + 18}{( x + 3 ) ( 2 x + 1 )}

36 + x^{2} y^{2} - 9 y^{2} - 4 x^{2}

a^{2} + 4 a

\frac{7}{8} - \frac{7}{12}

- 0.7 (- 9 q - 7 q + 5) - 0.4 q

\frac{4}{5} + \frac{5}{3}

What is 6/(2x+1)-x/(x+3) ?
The solution to 6/(2x+1)-x/(x+3) is (-2x^2+5x+18)/((x+3)(2x+1))