Question

I forgot what to do...

Simplify: \(\Huge\frac{x^2-4}{x^2+5x+6}\)

State any restrictions.

Answer 1

Factorize both denominator and numerator.
If there are common factors, you can cancel on condition that you state that the factor cannot have a value of zero.
Example:
(x^2-1)/(x+1) = (x+1)(x-1)/(x-1) =x+1 on condition that x\(\ne\)1

Answer 2

so I have \(\huge\frac{(x+2)(x-2)}{(x+2)(x+3)}\) so it's \(\huge\frac{x-2}{x+3}\) right?

Answer 3

@mathmate

Answer 4

how do I know the restrictions?

Answer 5

@rational

Answer 6

Before you cancel the common factor (x+2), the restriction is that the factor cannot be zero.

Answer 7

\(x+2 \ne 0\) also means x\(\ne\) -2.
This is the restriction.

Answer 8

but there's two restrictions... is the other one -3?

Answer 9

Some people would state the second restriction of x+3\(\ne\)0. (i.e. the other factor of the denominator).
I usually don't because it is an intrinsic restriction of the expression, not one arising from the simplification.

Answer 10

Note: -3 is not a restriction, x\(\ne\)-3 is.

Answer 11

yes, I know that it's \(x\cancel=-3\)

Answer 12

thank you