Question

How do you solve `-\frac { 5} { 3} = \frac { x ^ { 2} - 3} { x + 1}`?

Answer 1

`x=(-5+sqrt73)/6 color(white)(x) or color(white)(x)x=(-5-sqrt73)/6`

Explanation:

`-5/3 = (x^2 - 3)/(x + 1)`

Following these simple steps accordingly..

Cross Multiply

`-5(x + 1)= 3(x^2 - 3)`

While the minus `(-)` sign is attached to the `5` is because, in every fraction, the symbol always belongs to the numerator, if the denominator is removes..

Simplify...

`-5x - 5 = 3x^2 - 9`

Collect like terms

`3x^2 + 5x - 9 + 5 = 0`

`3x^2 + 5x - 4 = 0`

Solving the Quadratic Equation..

`x=(-b+-sqrt(b^2-4ac))/(2a)`

Where `a = 3, color(white)(x)b = 5, color(white)(x)c = -4`

`x=(-5+-sqrt(5^2-4(3)(-4)))/(2(3))`

`x=(-5+-sqrt(25 +48))/6`

`x=(-5+-sqrt73)/6`

`x=(-5+sqrt73)/6 color(white)(x) or color(white)(x)x=(-5-sqrt73)/6`