What is r/(r^2-4)+1/(r^2-6r+8) ?

The solution to r/(r^2-4)+1/(r^2-6r+8) is (r-1)/((r+2)(r-4))

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simplify r/(r^2-4)+1/(r^2-6r+8)

simplify

\frac{r}{r ^{2} - 4} + \frac{1}{r ^{2} - 6 r + 8}

\frac{r - 1}{( r + 2 ) ( r - 4 )}

Solution steps

\frac{r}{r ^{2} - 4} + \frac{1}{r ^{2} - 6 r + 8}

Least Common Multiplier of

r^{2} - 4, r^{2} - 6 r + 8 : (r + 2) (r - 2) (r - 4)

Adjust Fractions based on the LCM

= \frac{r ( r - 4 )}{( r + 2 ) ( r - 2 ) ( r - 4 )} + \frac{r + 2}{( r + 2 ) ( r - 2 ) ( r - 4 )}

Apply the fraction rule:

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

= \frac{r ( r - 4 ) + r + 2}{( r + 2 ) ( r - 2 ) ( r - 4 )}

Simplify

r (r - 4) + r + 2 : r^{2} - 3 r + 2

= \frac{r ^{2} - 3 r + 2}{( r + 2 ) ( r - 2 ) ( r - 4 )}

Cancel

\frac{r ^{2} - 3 r + 2}{( r + 2 ) ( r - 2 ) ( r - 4 )} : \frac{r - 1}{( r + 2 ) ( r - 4 )}

= \frac{r - 1}{( r + 2 ) ( r - 4 )}

\frac{1}{80} + \frac{1}{100}

\frac{x}{2} \times \frac{x}{2}

2 \times 32

\frac{3}{8} - \frac{3}{3 x + 4}

\frac{9 - 3 i}{1 + i}

What is r/(r^2-4)+1/(r^2-6r+8) ?
The solution to r/(r^2-4)+1/(r^2-6r+8) is (r-1)/((r+2)(r-4))