Question

What are the domain restrictions of the expression h^2+3h−10/h^2−12h+20 ?

Answer 1

Answer:

h≠10.

Step-by-step explanation:

The expression is

$\frac{h^2+3h-10}{h^2-12h+20}.$

To find the restrictions we can factor the numerator and the denominator by searching two numbers that multiplied are -10 and subtracted are 3, also for the denominator:

$\frac{h^2+3h-10}{h^2-12h+20}= \frac{(h+5)(h-2)}{(h-10)(h-2)} = \frac{(h+5)}{(h-10)}.$

When we have a fraction the denominator can not be zero. Then, for our expression h needs to be different to 10 or the denominator would be zero.

Answer 2

The denominator cannot be 0, so if h^2-12h+20=0
(h-2)(h-10)=0
h=2 or h=10
So h cannot be 2 or 10, the first and third choices are correct.