simplify the complex fraction
4/x+5 +2
_________
14/x+5 -2
Once i multiply by the LCD i get
4+2(x+5)/14-2(x+5)
however i can't see what i can do next to simplify can you explain.
well, geez -- get rid of the parentheses and collect terms!
4+2(x+5) / 14-2(x+5)
= 4+2x+10 / 14-2x-10
= 14+2x / 4-2x
= (7+x)/(2-x)
To simplify the complex fraction (4/(x+5) + 2) / (14/(x+5) - 2), you're on the right track by multiplying both the numerator and denominator by the LCD, which is (x+5).
The result you obtained, (4+2(x+5))/(14-2(x+5)), can now be simplified further.
First, distribute the 2 to both terms inside the parentheses in the numerator and denominator:
(4+2x+10)/(14-2x-10)
Now simplify within the numerator and denominator:
(2x+14)/(4-2x)
Next, factor out a 2 from both terms in the numerator:
2(x+7)/(4-2x)
Then, notice that the numerator and denominator have a common factor of 2. Divide both terms by 2 to cancel out the common factor:
(x+7)/(2-x)
Finally, rearrange the terms in the denominator to have a positive x:
(x+7)/(-x+2)
Thus, the simplified form of the complex fraction is (x+7)/(-x+2).