What is (2x+4)/(5x+2)-(2x+1)/(x-3) ?

The solution to (2x+4)/(5x+2)-(2x+1)/(x-3) is (-8x^2-11x-14)/((x-3)(5x+2))

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simplify (2x+4)/(5x+2)-(2x+1)/(x-3)

simplify

\frac{2 x + 4}{5 x + 2} - \frac{2 x + 1}{x - 3}

\frac{- 8 x ^{2} - 11 x - 14}{( x - 3 ) ( 5 x + 2 )}

Solution steps

\frac{2 x + 4}{5 x + 2} - \frac{2 x + 1}{x - 3}

Least Common Multiplier of

5 x + 2, x - 3 : (x - 3) (5 x + 2)

Adjust Fractions based on the LCM

= \frac{( 2 x + 4 ) ( x - 3 )}{( x - 3 ) ( 5 x + 2 )} - \frac{( 2 x + 1 ) ( 5 x + 2 )}{( x - 3 ) ( 5 x + 2 )}

Apply the fraction rule:

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

= \frac{( 2 x + 4 ) ( x - 3 ) - ( 2 x + 1 ) ( 5 x + 2 )}{( x - 3 ) ( 5 x + 2 )}

Simplify

(2 x + 4) (x - 3) - (2 x + 1) (5 x + 2) : - 8 x^{2} - 11 x - 14

= \frac{- 8 x ^{2} - 11 x - 14}{( x - 3 ) ( 5 x + 2 )}

- 354 \cdot (- 2) 3

9 x^{4} - x^{2}

(4 x + 1) (2 x + 6)

3 x^{2} \cdot 3 x

What is (2x+4)/(5x+2)-(2x+1)/(x-3) ?
The solution to (2x+4)/(5x+2)-(2x+1)/(x-3) is (-8x^2-11x-14)/((x-3)(5x+2))