If x>3, which of the following is equivalent to 2B%5Cfrac%7B1%7D%7Bx%2B3%7D%7D" id="TexFormula1" title="\frac{1}{\frac{1}{x+2}+\frac{1}{x+3}}" alt="\frac{1}{\frac{1}{x+2}+\frac{1}{x+3}}" align="absmiddle" class="latex-formula">?
A)
B)
C)
D)
2 answers:
Answer:
B.
Step-by-step explanation:
Add the fractions in the denominator.
Denominators are equal, so combine.
Combine like terms.
Back to the problem.
Apply fraction rule 1/b/c = c/b
Expand the brackets in the numerator.
Answer:
x^2 +5x+6
----------------------
2x+5
Step-by-step explanation:
1
-----------------
1/(x+2) + 1/(x+3)
Multiply by ( x+2) * (x+3) in the numerator and denominator
1 * ( x+2) * (x+3)
-----------------
(1/(x+2) + 1/(x+3)) *( x+2) * (x+3)
Distribute
( x+2) * (x+3)
-----------------
((x+3) + (x+2))
Combine like terms
( x+2) * (x+3)
-----------------
2x+5
Foil the numerator
x^2 +2x+3x+6
---------------------
2x+5
Combine like terms
x^2 +5x+6
----------------------
2x+5
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Hope this helps!
=)