Question

How do you evaluate `y= \frac { 2x ^ { 2} - x + 5} { x ^ { 2} - 1}`?

Answer 1

`2+(7-x)/(x^2-1)`

Explanation:

`"one way is to use the divisor as a factor in the numerator"`

`"consider the numerator"`

`color(red)(2)(x^2-1)color(magenta)(+2)-x+5`

`=color(red)(2)(x^2-1)-x+7`

`"quotient "=color(red)(2)," remainder "=-x+7=7-x`

`rArr(2x^2-x+5)/(x^2-1)=2+(7-x)/(x^2-1)`