Question

Add and simplify and please write out all of your steps.
5x-12/ x^2-16 + -8/x^2-16

Answer 1

Some please help ):

Answer 2

\(\bf \cfrac{5x-12}{x^2-16}+\cfrac{-8}{x^2-16}?\)

Answer 3

Could you explain how to solve it to me? I'm very confused

Answer 4

ok... do you know the differences of squares yet?
as in \(\bf \textit{difference of squares}
\\ \quad \\
(a-b)(a+b) = a^2-b^2\qquad \qquad
a^2-b^2 = (a-b)(a+b)\)

Answer 5

Yes

Answer 6

ok... well then
\(\bf \cfrac{5x-12}{x^2-16}+\cfrac{-8}{x^2-16}
\\ \quad \\
{\color{brown}{ \cfrac{a}{b}+\cfrac{c}{b}\implies \cfrac{a+c}{b} }}\qquad thus
\\ \quad \\
\cfrac{5x-12}{x^2-16}+\cfrac{-8}{x^2-16}\implies \cfrac{(5x-12)+(-8)}{x^2-16}\qquad {\color{brown}{ 16=4^2}}\qquad thus
\\ \quad \\
\cfrac{5x-12-8}{x^2-{\color{brown}{ 4^2}}}\implies \cfrac{5x-20}{(x-4)(x+4)}\implies ?\)

Answer 7

notice the numerator
you can take a common factor
what do you think it is?

Answer 8

5?

Answer 9

anyhow.. need to dash... as you can see, is 5, yes, for the common factor of the numerator
thus
\(\bf \cfrac{5x-12-8}{x^2-{\color{brown}{ 4^2}}}\implies \cfrac{5x-20}{(x-4)(x+4)}\implies \cfrac{5\cancel{(x-4)}}{\cancel{(x-4)}(x+4)}\)

Answer 10

So 5/x+4 is the answer?

Answer 11

Also could you help me with another problem?

Answer 12

Subtract and simplify 4y/y^2-6y+8 - 16/y^2-6y+8