What is (7x)/(x-7)+(7x+3)/(x-6) ?

The solution to (7x)/(x-7)+(7x+3)/(x-6) is (14x^2-88x-21)/((x-7)(x-6))

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simplify (7x)/(x-7)+(7x+3)/(x-6)

simplify

\frac{7 x}{x - 7} + \frac{7 x + 3}{x - 6}

\frac{14 x ^{2} - 88 x - 21}{( x - 7 ) ( x - 6 )}

Solution steps

\frac{7 x}{x - 7} + \frac{7 x + 3}{x - 6}

Least Common Multiplier of

x - 7, x - 6 : (x - 7) (x - 6)

Adjust Fractions based on the LCM

= \frac{7 x ( x - 6 )}{( x - 7 ) ( x - 6 )} + \frac{( 7 x + 3 ) ( x - 7 )}{( x - 7 ) ( x - 6 )}

Apply the fraction rule:

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

= \frac{7 x ( x - 6 ) + ( 7 x + 3 ) ( x - 7 )}{( x - 7 ) ( x - 6 )}

Simplify

7 x (x - 6) + (7 x + 3) (x - 7) : 14 x^{2} - 88 x - 21

= \frac{14 x ^{2} - 88 x - 21}{( x - 7 ) ( x - 6 )}

\frac{5}{50}

1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10

(2 x - 1)^{5}

(4 x^{2} + 9 x - 7) - (- 7 x^{2} + 5 x - 1)

\frac{200}{3}

What is (7x)/(x-7)+(7x+3)/(x-6) ?
The solution to (7x)/(x-7)+(7x+3)/(x-6) is (14x^2-88x-21)/((x-7)(x-6))