SOLUTION: I'm really having trouble with these few problems here and I can't call anyone from my Algebra class that I know because they're all busy, so I was hoping that someone could help m

Algebra ->  Expressions-with-variables -> SOLUTION: I'm really having trouble with these few problems here and I can't call anyone from my Algebra class that I know because they're all busy, so I was hoping that someone could help m      Log On


   

Question 81902This question is from textbook Algebra 1
: I'm really having trouble with these few problems here and I can't call anyone from my Algebra class that I know because they're all busy, so I was hoping that someone could help me? If you can you would forever have my gratitude!!
10. x/x^2-3=5/x+4 I know there is two answers to this problem
14. 4w/3w-2+2w/3w+2=2 I know the answer is w=4.
16. 12/x^2-16-3=24/x-4 The answers are -6 and -2.
Please, please tell me how to do these problems!! This question is from textbook Algebra 1

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
10. Solve for x:
x%2F%28x%5E2-3%29+=+5%2F%28x%2B4%29 Multiply both sides by%28x%5E2-3%29%28x%2B4%29
Cancel as indicated and simplify.
x%28x%2B4%29+=+5%28x%5E2-3%29
x%5E2%2B4x+=+5x%5E2-15 Subtract x^2 from both sides.
4x+=+4x%5E2-15 Subtract 4x from both sides.
4x%5E2-4x-15+=+0 Factor this quadratic equation.
%282x%2B3%29%282x-5%29+=+0 Apply the zero products principle.
2x%2B3+=+0 and/or 2x-5+=+0
2x+=+-3 so x+=+-3%2F2
2x+=+5 so x+=+5%2F2
Solutions:
x+=+-3%2F2
x+=+5%2F2
14. Solve for w:
4w%2F%283w-2%29+%2B+2w%2F%283w%2B2%29+=+2 Multiply both sides by%283w-2%29%283w%2B2%29
Simplify.
4w%283w%2B2%29+%2B+2w%283w-2%29+=+2%289w%5E2-4%29
%2812w%5E2%2B8w%29+%2B+%286w%5E2-4w%29+=+18w%5E2-8
%2818w%5E2%29%2B4w+=+%2818w%5E2%29-8 Subtract18w%5E2 from both sides.
4w+=+-8 Divide both sides by 4.
w+=+-2
16. Solve for x:
12%2F%28x%5E2-16%29+-+3+=+24%2F%28x-4%29
%2812-3%28x%5E2-16%29%29%2F%28x%5E2-16%29+=+24%2F%28x-4%29 Simplify.
%2812-3x%5E2-48%29%2F%28x%2B4%29%28x-4%29+=+24%28x%2B4%29%2F%28x-4%29%28x%2B4%29
12-3x%5E2-48+=+24x%2B96
3x%5E3%2B24x%2B36+=+0 Simplify by factoring out a 3.
x%5E2%2B8x%2B12+=+0 Factor this quadratic equation.
%28x%2B2%29%28x%2B6%29+=+0 Apply the zero products principle.
x%2B2+=+0 and/orx%2B6+=+0
Solutions:
x+=+-2
x+=+-6