What is 7/(x-3)+(3x+1)/(x-5) ?

The solution to 7/(x-3)+(3x+1)/(x-5) is (3x^2-x-38)/((x-3)(x-5))

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simplify 7/(x-3)+(3x+1)/(x-5)

simplify

\frac{7}{x - 3} + \frac{3 x + 1}{x - 5}

\frac{3 x ^{2} - x - 38}{( x - 3 ) ( x - 5 )}

Solution steps

\frac{7}{x - 3} + \frac{3 x + 1}{x - 5}

Least Common Multiplier of

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

Adjust Fractions based on the LCM

= \frac{7 ( x - 5 )}{( x - 3 ) ( x - 5 )} + \frac{( 3 x + 1 ) ( x - 3 )}{( x - 3 ) ( x - 5 )}

Apply the fraction rule:

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

= \frac{7 ( x - 5 ) + ( 3 x + 1 ) ( x - 3 )}{( x - 3 ) ( x - 5 )}

Simplify

7 (x - 5) + (3 x + 1) (x - 3) : 3 x^{2} - x - 38

= \frac{3 x ^{2} - x - 38}{( x - 3 ) ( x - 5 )}

(a + 3) (a + 1) - 4 (a + 1)

3. 3^{2}

3 x - x^{3}

(x + 1) (x - 2) (x - 4)

(- 3 sin (t))^{2}

What is 7/(x-3)+(3x+1)/(x-5) ?
The solution to 7/(x-3)+(3x+1)/(x-5) is (3x^2-x-38)/((x-3)(x-5))