Question

If x ≠ -2, then 5x2 -20/5x+10 =​

Answer 1

Answer:

$x-2\, ,x\neq -2$

Step-by-step explanation:

So we have the expression:

$\frac{5x^2-20}{5x+10}\, ,x\neq -2$

For both the numerator and the denominator, factor out a 5:

$\frac{5(x^2-4)}{5(x+2)}\, ,x\neq-2$

The term in the numerator can be factored. This is the difference of two squares pattern:

$\frac{5(x-2)(x+2)}{5(x+2)}\, ,x\neq-2$

Both layers have a 5(x+2). Cancel them, Since we know that x cannot be -2, we can safely do so:

$x-2\, ,x\neq -2$

And we're done!

Notes:

If we weren't told that x ≠ -2, then we cannot divide them because if x did equal -2, the equation would be undefined. However, since we were given that, we can simplify.

However, even if we weren't given x ≠ -2, we can still simplify, but we need to add the restraint ourselves. This must be done, or else the equation won't be correct.