What is x/(x^2-49)+(3x+1)/(x+7) ?

The solution to x/(x^2-49)+(3x+1)/(x+7) is (3x^2-19x-7)/((x+7)(x-7))

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simplify x/(x^2-49)+(3x+1)/(x+7)

simplify

\frac{x}{x ^{2} - 49} + \frac{3 x + 1}{x + 7}

\frac{3 x ^{2} - 19 x - 7}{( x + 7 ) ( x - 7 )}

Solution steps

\frac{x}{x ^{2} - 49} + \frac{3 x + 1}{x + 7}

Least Common Multiplier of

x^{2} - 49, x + 7 : (x + 7) (x - 7)

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

x + (3 x + 1) (x - 7) : 3 x^{2} - 19 x - 7

= \frac{3 x ^{2} - 19 x - 7}{( x + 7 ) ( x - 7 )}

\frac{21}{12}

\frac{21}{56}

\frac{55}{2}

lo g_{10} (10 0^{8})

What is x/(x^2-49)+(3x+1)/(x+7) ?
The solution to x/(x^2-49)+(3x+1)/(x+7) is (3x^2-19x-7)/((x+7)(x-7))