anonymous
  • anonymous
Add and simplify and please write out all of your steps. 5x-12/ x^2-16 + -8/x^2-16
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
Some please help ):
jdoe0001
  • jdoe0001
\(\bf \cfrac{5x-12}{x^2-16}+\cfrac{-8}{x^2-16}?\)
anonymous
  • anonymous
Could you explain how to solve it to me? I'm very confused

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jdoe0001
  • jdoe0001
ok... do you know the differences of squares yet? as in \(\bf \textit{difference of squares} \\ \quad \\ (a-b)(a+b) = a^2-b^2\qquad \qquad a^2-b^2 = (a-b)(a+b)\)
anonymous
  • anonymous
Yes
jdoe0001
  • jdoe0001
ok... well then \(\bf \cfrac{5x-12}{x^2-16}+\cfrac{-8}{x^2-16} \\ \quad \\ {\color{brown}{ \cfrac{a}{b}+\cfrac{c}{b}\implies \cfrac{a+c}{b} }}\qquad thus \\ \quad \\ \cfrac{5x-12}{x^2-16}+\cfrac{-8}{x^2-16}\implies \cfrac{(5x-12)+(-8)}{x^2-16}\qquad {\color{brown}{ 16=4^2}}\qquad thus \\ \quad \\ \cfrac{5x-12-8}{x^2-{\color{brown}{ 4^2}}}\implies \cfrac{5x-20}{(x-4)(x+4)}\implies ?\)
jdoe0001
  • jdoe0001
notice the numerator you can take a common factor what do you think it is?
anonymous
  • anonymous
5?
jdoe0001
  • jdoe0001
anyhow.. need to dash... as you can see, is 5, yes, for the common factor of the numerator thus \(\bf \cfrac{5x-12-8}{x^2-{\color{brown}{ 4^2}}}\implies \cfrac{5x-20}{(x-4)(x+4)}\implies \cfrac{5\cancel{(x-4)}}{\cancel{(x-4)}(x+4)}\)
anonymous
  • anonymous
So 5/x+4 is the answer?
anonymous
  • anonymous
Also could you help me with another problem?
anonymous
  • anonymous
Subtract and simplify 4y/y^2-6y+8 - 16/y^2-6y+8

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