rational expressions: find (3x)/(x + 3) + (x + 2)/(x - 7)

jhawk555

New member
Joined
Sep 26, 2006
Messages
34
I am stuck in the middle of my problem. Was hoping that someone could check my work.

Find: (3x)/(x + 3) + (x + 2)/(x - 7)

My work:

. . .[3x(x - 7) + (x + 2)(x + 3)] / [(x + 3)(x - 7)]

. . .(3x^2 - 21x + x^2 + 3x + 2x + 6) / [(x + 3)(x - 7)]

. . .(4x^2 - 16x + 6) / [(x + 3)(x - 7)]

I need to reduce the top line to lowest terms.

. . .2(x^2 - 8x + 3) = 2(2x - 3)(x - 1)

...or (2x-?) (2x - ?)

This is where I am mixed up and could use some guidance.

Still trying to figure this out. Thanks in advance.
 

galactus

Super Moderator
Staff member
Joined
Sep 28, 2005
Messages
7,216
You got 'er whittled down to:

\(\displaystyle \L\\\frac{2(2x^{2}-8x+3)}{(x+3)(x-7)}=0\)

Now, I believe the kibosh has been put on factoring the numerator any further.

Use the quadratic formula on the numerator. Maybe complete the square.
 
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