Question

Find the sum of all $r$ such that $\frac{8r^2 - 14 r + 3}{r+5} = 4r -1$.

Answer 1

8.25

Explanation:

`(8r^2 - 14 r + 3)/(r+5) = 4r -1`

`8r^2 - 14r + 3= (4r -1)(r + 5)`

`8r^2 - 14r + 3= 4 {r}^(2) + 19r - 5`

`4 {r}^(2) - 33r + 8=0`

`4 {r}^(2) - 32r - r + 8 = 0`

`4r(r - 8) - 1(r - 8) = 0`

`(4r - 1)(r - 8)`

`r = 8 \: or \: (1)/(4)`

Therefore the sum of all values of r

`8 + (1)/(4) = 8 (1)/(4)`