SOLUTION: please help me with this problem. im getting confused. and i really need ur help. solve x-4 4 29 ---- + ---- = ---- x+1 x 30 please show the work so

Algebra ->  Test -> SOLUTION: please help me with this problem. im getting confused. and i really need ur help. solve x-4 4 29 ---- + ---- = ---- x+1 x 30 please show the work so      Log On


   

Question 173382: please help me with this problem. im getting confused. and i really need ur help.
solve
x-4 4 29
---- + ---- = ----
x+1 x 30

please show the work so i can understand it. thank you !!!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

%28x-4%29%2F%28x%2B1%29%2B%284%29%2F%28x%29=%2829%29%2F%2830%29 Start with the given equation.


Multiply every term on both sides by the LCD 30x%28x%2B1%29. Doing this will eliminate all of the fractions.


30x%28x-4%29%2B30%2A4%28x%2B1%29=29x%28x%2B1%29 Simplify.


30x%28x-4%29%2B120%28x%2B1%29=29x%28x%2B1%29 Multiply.


30x%5E2-120x%2B120x%2B120=29x%5E2%2B29x Distribute.


30x%5E2-120x%2B120x%2B120=29x%5E2%2B29x Start with the given equation.


30x%5E2-120x%2B120x%2B120-29x%5E2-29x=0 Subtract 29x%5E2 from both sides. Subtract 29x from both sides.


x%5E2-29x%2B120=0 Combine like terms.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=1, b=-29, and c=120


Let's use the quadratic formula to solve for x


x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


x+=+%28-%28-29%29+%2B-+sqrt%28+%28-29%29%5E2-4%281%29%28120%29+%29%29%2F%282%281%29%29 Plug in a=1, b=-29, and c=120


x+=+%2829+%2B-+sqrt%28+%28-29%29%5E2-4%281%29%28120%29+%29%29%2F%282%281%29%29 Negate -29 to get 29.


x+=+%2829+%2B-+sqrt%28+841-4%281%29%28120%29+%29%29%2F%282%281%29%29 Square -29 to get 841.


x+=+%2829+%2B-+sqrt%28+841-480+%29%29%2F%282%281%29%29 Multiply 4%281%29%28120%29 to get 480


x+=+%2829+%2B-+sqrt%28+361+%29%29%2F%282%281%29%29 Subtract 480 from 841 to get 361


x+=+%2829+%2B-+sqrt%28+361+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%2829+%2B-+19%29%2F%282%29 Take the square root of 361 to get 19.


x+=+%2829+%2B+19%29%2F%282%29 or x+=+%2829+-+19%29%2F%282%29 Break up the expression.


x+=+%2848%29%2F%282%29 or x+=++%2810%29%2F%282%29 Combine like terms.


x+=+24 or x+=+5 Simplify.


So the answers are x+=+24 or x+=+5