Solve r^2+4r-9/r^2-8r+7--3r^2+5r-6/r^2-8r+7

$$\frac { r ^ { 2 } + 4 r - 9 } { r ^ { 2 } - 8 r + 7 } - \frac { - 3 r ^ { 2 } + 5 r - 6 } { r ^ { 2 } - 8 r + 7 }$$

Evaluate

$$\frac{4r+3}{r-7}$$

Short Solution Steps

Since \frac{r^{2}+4r-9}{r^{2}-8r+7} and \frac{-3r^{2}+5r-6}{r^{2}-8r+7} have the same denominator, subtract them by subtracting their numerators.

$$\frac{r^{2}+4r-9-\left(-3r^{2}+5r-6\right)}{r^{2}-8r+7}$$

Do the multiplications in r^{2}+4r-9-\left(-3r^{2}+5r-6\right).

$$\frac{r^{2}+4r-9+3r^{2}-5r+6}{r^{2}-8r+7}$$

Combine like terms in r^{2}+4r-9+3r^{2}-5r+6.

$$\frac{4r^{2}-r-3}{r^{2}-8r+7}$$

Factor the expressions that are not already factored in \frac{4r^{2}-r-3}{r^{2}-8r+7}.

$$\frac{\left(r-1\right)\left(4r+3\right)}{\left(r-7\right)\left(r-1\right)}$$

Cancel out r-1 in both numerator and denominator.

$$\frac{4r+3}{r-7}$$

Expand

$$\frac{4r+3}{r-7}$$

Short Solution Steps

Since \frac{r^{2}+4r-9}{r^{2}-8r+7} and \frac{-3r^{2}+5r-6}{r^{2}-8r+7} have the same denominator, subtract them by subtracting their numerators.

$$\frac{r^{2}+4r-9-\left(-3r^{2}+5r-6\right)}{r^{2}-8r+7}$$

Do the multiplications in r^{2}+4r-9-\left(-3r^{2}+5r-6\right).

$$\frac{r^{2}+4r-9+3r^{2}-5r+6}{r^{2}-8r+7}$$

Combine like terms in r^{2}+4r-9+3r^{2}-5r+6.

$$\frac{4r^{2}-r-3}{r^{2}-8r+7}$$

Factor the expressions that are not already factored in \frac{4r^{2}-r-3}{r^{2}-8r+7}.

$$\frac{\left(r-1\right)\left(4r+3\right)}{\left(r-7\right)\left(r-1\right)}$$

Cancel out r-1 in both numerator and denominator.

$$\frac{4r+3}{r-7}$$