## Adding/Subtracting Rational Expressions w Unlike Denominator

Quadratic equations and inequalities, variation equations, function notation, systems of equations, etc.
onmyown
Posts: 18
Joined: Fri Dec 17, 2010 10:16 pm
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### Adding/Subtracting Rational Expressions w Unlike Denominator

Hi, Can someone please show me how this problem is solved:

Here is one of my attempts:
First, I found LCD, so I can subtract the two expressions. I did so by multiplying (m-6) to (m^2-36) and (m^2-36) to (m-6) in the denominators. I also multiplied the numerators of each fraction by the same binomial their denominators were multiplied by in order to get to the LCD.
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Second, I simplified each numerator and combined the two expressions into one, with the LCD as the denominator.
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Third, I simplified the numerator of the expression.
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However, this is not the solution. The correct answer is actually:
Can someone please explain to me how to solve this problem?

Martingale
Posts: 350
Joined: Mon Mar 30, 2009 1:30 pm
Location: USA
Contact:

### Re: Adding/Subtracting Rational Expressions w Unlike Denomin

onmyown wrote:Hi, Can someone please show me how this problem is solved:

Here is one of my attempts:
First, I found LCD, so I can subtract the two expressions. I did so by multiplying (m-6) to (m^2-36) and (m^2-36) to (m-6) in the denominators. I also multiplied the numerators of each fraction by the same binomial their denominators were multiplied by in order to get to the LCD.
=
Second, I simplified each numerator and combined the two expressions into one, with the LCD as the denominator.
=
Third, I simplified the numerator of the expression.
=

However, this is not the solution. The correct answer is actually:
Can someone please explain to me how to solve this problem?

$\frac{7m(m-6)-3(m^2-36)}{(m^2-36)(m-6)}$

$=\frac{7m(m-6)-3(m-6)(m+6)}{(m^2-36)(m-6)}$

$=\frac{(7m-3(m+6))(m-6)}{(m^2-36)(m-6)}$

$=\frac{(7m-3(m+6))}{(m^2-36)}$

$=\frac{7m-3m-18}{(m^2-36)}$

$=\frac{4m-18}{(m^2-36)}$