SOLUTION: Okay, second time asking for help with this particular question. 2x+1/x^2-16 [+] x^2-6x-7/x^2-11x+28 I placed the + in [] just so you could tell the two fraction apart, it

Question 132040: Okay, second time asking for help with this particular question.
2x+1/x^2-16 [+] x^2-6x-7/x^2-11x+28
I placed the + in [] just so you could tell the two fraction apart, it does not mean anything.
Found 3 solutions by stanbon, rapaljer, bucky:
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
2x+1/x^2-16 [+] x^2-6x-7/x^2-11x+28
-------------------------------------
Factor where you can:
[(2x+1)/(x-4)(x+4)] + [(x-7)(x+1)/(x-4)(x-7)]
----------------------------
Least common denominator: (x-4)(x+4)(x-7)
--------------------------
Rewrite each fraction with the lcm as its denominator.
[(2x+1)(x-7)/lcm] + [(x-7)(x+1)(x+4)]/lcm
------------------------------
Simplify:
[2x^2-13x-7+(x-7)(x^2+5x+4)]/lcm
---------
[2x^2-13x-7+x^3+5x^2-7x^2+4x-35x-28]/lcm
[x^3-44x-35]/lcm
==================
Cheers,
Stan H.
Answer by rapaljer(4671)   (Show Source): You can put this solution on YOUR website!

Reduce the second fraction, which simplifies the LCD:

The LCD = (x-4)(x+4)

See my own website, click on my tutor name "rapaljer" anywhere in algebra.com. Go to the first link on my homepage which is "Basic and Intermediate Algebra: One Step at a Time". Look in Chapter 3 of Basic Algebra, for the Section 3.03 "Finding the LCD" and 3.04 "Adding and Subtracting Fractions."

R^2

Answer by bucky(2189)   (Show Source): You can put this solution on YOUR website!
Given:
.

.
Factor the denominators of both fractions and the numerator of the second fractions. They
factor as follows:
.

.
Substitute these factors at the appropriate places in the original equation and you get:
.

.
Notice that in the second fraction the term (x -7) appears in both the numerator and the
denominator. Therefore, it can be canceled out as follows:
.

.
and the problem is then reduced to:
.

.
The second fraction can be put over a common denominator of by multiplying
it by . Notice that since the numerator of this multiplier is the same as
the denominator, the multiplier is equivalent to 1 so it doesn't really change the second fraction.
The multiplication is as follows:
.

.
and this becomes:
.

.
Notice now that the two fractions have the common denominator of
so the numerators can be combined over this common denominator to get:
.

.
Simplify the numerator by multiplying out the two factors to make the expression become:
.

.
In the numerator combine the 2x and the 5x to get +7x and combine the 1 and the 4 to get +5.
Substitute these results and you get the answer of:
.

.
This is the answer. The numerator does not factor.
.
Or you can, if you so desire, multiply out the denominator to get the answer of:
.

.
Hope this helps you to see your way through the problem.
.
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