SOLUTION: Solve. 9/x-5 -1 = 8/x+5 Can anyone help me figure these fractions out, so i CAN HAVE A FORMULA for future references, the slashes are fraction bars.

Algebra ->  Numeric Fractions Calculators, Lesson and Practice -> SOLUTION: Solve. 9/x-5 -1 = 8/x+5 Can anyone help me figure these fractions out, so i CAN HAVE A FORMULA for future references, the slashes are fraction bars.      Log On


   

Question 103817: Solve.

9/x-5 -1 = 8/x+5
Can anyone help me figure these fractions out, so i CAN HAVE A FORMULA for future references, the slashes are fraction bars.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
9%2F%28x-5+%29-1+=+8%2F%28x%2B5%29 simplifies to 9%2F%28x-5%29-8%2F%28x%2B5%29-1=0

The least common denominator is %28x-5%29%28x%2B5%29

%289%28x%2B5%29+-+8%28x-5%29+-+1%28x-5%29%28x%2B5%29%29%2F%28x-5%29%28x%2B5%29+=+0 now both sides multiply by %28x-5%29%28x%2B5%29 and you will have
%289%28x%2B5%29+-+8%28x-5%29+-+1%28x-5%29%28x%2B5%29%29%2F%28x-5%29%28x%2B5%29+=+0 /* %28x-5%29%28x%2B5%29
this will eliminate denominator, and you will have
%289%28x%2B5%29+-+8%28x-5%29+-+1%28x-5%29%28x%2B5%29%29+=+0
9x+%2B+45+-+8x+%2B+40+-+%28x%5E2%2B+5x+-5x+-25%29+=+0
x+%2B+85+-+x%5E2+%2B+25+=+0
-+x%5E2+%2B+x+%2B+110+=+0

now you can use quadratic formula to find x1 and x2, then you can graf it

Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for x:


Starting with the general quadratic


ax%5E2%2Bbx%2Bc=0


the general solution using the quadratic equation is:


x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29




So lets solve -x%5E2%2Bx%2B110=0 ( notice a=-1, b=1, and c=110)





x+=+%28-1+%2B-+sqrt%28+%281%29%5E2-4%2A-1%2A110+%29%29%2F%282%2A-1%29 Plug in a=-1, b=1, and c=110




x+=+%28-1+%2B-+sqrt%28+1-4%2A-1%2A110+%29%29%2F%282%2A-1%29 Square 1 to get 1




x+=+%28-1+%2B-+sqrt%28+1%2B440+%29%29%2F%282%2A-1%29 Multiply -4%2A110%2A-1 to get 440




x+=+%28-1+%2B-+sqrt%28+441+%29%29%2F%282%2A-1%29 Combine like terms in the radicand (everything under the square root)




x+=+%28-1+%2B-+21%29%2F%282%2A-1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%28-1+%2B-+21%29%2F-2 Multiply 2 and -1 to get -2


So now the expression breaks down into two parts


x+=+%28-1+%2B+21%29%2F-2 or x+=+%28-1+-+21%29%2F-2


Lets look at the first part:


x=%28-1+%2B+21%29%2F-2


x=20%2F-2 Add the terms in the numerator

x=-10 Divide


So one answer is

x=-10




Now lets look at the second part:


x=%28-1+-+21%29%2F-2


x=-22%2F-2 Subtract the terms in the numerator

x=11 Divide


So another answer is

x=11


So our solutions are:

x=-10 or x=11