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

1. anonymous

2. jdoe0001

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

3. anonymous

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

4. jdoe0001

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

5. anonymous

Yes

6. jdoe0001

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

7. jdoe0001

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

8. anonymous

5?

9. jdoe0001

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

10. anonymous

11. anonymous

Also could you help me with another problem?

12. anonymous

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