What is (7r)/(r-2)-(2r)/(r-3) ?

The solution to (7r)/(r-2)-(2r)/(r-3) is (5r^2-17r)/((r-2)(r-3))

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simplify (7r)/(r-2)-(2r)/(r-3)

simplify

\frac{7 r}{r - 2} - \frac{2 r}{r - 3}

\frac{5 r ^{2} - 17 r}{( r - 2 ) ( r - 3 )}

Solution steps

\frac{7 r}{r - 2} - \frac{2 r}{r - 3}

Least Common Multiplier of

r - 2, r - 3 : (r - 2) (r - 3)

Adjust Fractions based on the LCM

= \frac{7 r ( r - 3 )}{( r - 2 ) ( r - 3 )} - \frac{2 r ( r - 2 )}{( r - 2 ) ( r - 3 )}

Apply the fraction rule:

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

= \frac{7 r ( r - 3 ) - 2 r ( r - 2 )}{( r - 2 ) ( r - 3 )}

Simplify

7 r (r - 3) - 2 r (r - 2) : 5 r^{2} - 17 r

= \frac{5 r ^{2} - 17 r}{( r - 2 ) ( r - 3 )}

2 \times 3

\frac{128}{27} - \frac{64}{9}

517 + 42 - 17 - 42

43 \times 3

2 \times \frac{3}{8}

What is (7r)/(r-2)-(2r)/(r-3) ?
The solution to (7r)/(r-2)-(2r)/(r-3) is (5r^2-17r)/((r-2)(r-3))