x+5/x-5 - x-5/x+5 = 15/4
Answers
Answered by
5
Answer:
NO solution
Step-by-step explanation:
To solve this problem, first you have to isolate by the x from one side of the equation.
First, least common multiple of x is 4x.
x*4x+5/x*4x-5*4x-x*4x-5/x*4x+5*4x=15/4*4x
Solve.
0=15x
Next, switch sides.
15x=0
Then, divide by 15 from both sides.
15x/15=0/15
Solve.
0/15=0
Therefore, there are NO solutions and x=0, which is our answer.
Hope this helps!
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Answered by
5
x+5/x-5 - x-5/x+5 = 15/4
{(x+5)^2 - (x -5)^2}/x^2 -25 = 15/4
(x+5+x-5)(x+5-x +5) /(x-5)(x+5)=15/4
20x/(x^2 -25)=15/4
15x^2 - 375 -80x= 0
3x^2 - 75 - 16x =0
9x^2 - 48x + 8^2 - 139=0
(3x - 8)^2 -( sqrt139)^2=0
(3x - 8 + sqrt139)(3x -( 8 +sqrt139))=0
x = (8 - sqrt139)/3
and (8+sqrt139)/3
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