SOLUTION: how do i solve for x: x/(x-5)-2/(x+5)=50/(x^2-25)

Algebra ->  Rational-functions -> SOLUTION: how do i solve for x: x/(x-5)-2/(x+5)=50/(x^2-25)       Log On


   

Question 701287: how do i solve for x: x/(x-5)-2/(x+5)=50/(x^2-25)


Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
+x%2F%28x-5%29-2%2F%28x%2B5%29=50%2F%28x%5E2-25%29....common denominator for x-5 and x%2B5 %28x-5%29%28x%2B5%29

....since %28x-5%29%28x%2B5%29=%28x%5E2-25%29, we will have


+%28x%28x%2B5%29-2%28x-5%29%29%2F%28x%5E2-25%29%29=50%2F%28x%5E2-25%29

+%28x%5E2%2B5x-2x%2B5%29%2F%28x%5E2-25%29%29=50%2F%28x%5E2-25%29

+%28x%5E2%2B3x%2B5%29%2F%28x%5E2-25%29%29=50%2F%28x%5E2-25%29.....cross multiply

+%28x%5E2%2B3x%2B5%29%28x%5E2-25%29=50%28x%5E2-25%29

x%5E4-25x%5E2%2B3x%5E3-75x%2B5x%5E2-125=50x%5E2-1250

x%5E4-25x%5E2%2B3x%5E3-75x%2B5x%5E2-125-50x%5E2%2B1250=0

x%5E4%2B3x%5E3-70x%5E2-75x%2B1125=0

%283x%5E3-75x%29%2Bx%5E4-70x%5E2%2B1125=0

3x%28x%5E2-25%29%2B%28x%5E4-25x%5E2%29-%2845x%5E2-1125%29=0


3x%28x%5E2-25%29%2Bx%5E2%28x%5E2-25%29-45%28x%5E2-25%29=0

%28x%5E2-25%29%28x%5E2%2B3x-45%29=0

%28x-5%29%28x%2B5%29%28x%5E2%2B3x-45%29=0

solutions:
if %28x-5%29=0....=>...x=5
if %28x%2B5%29=0....=>...x=-5
if %28x%5E2%2B3x-45%29=0, ...we need to use quadratic formula to find zeros

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

x+=+%28-3+%2B-+sqrt%28+3%5E2-4%2A1%2A%28-45%29+%29%29%2F%282%2A1%29+

x+=+%28-3+%2B-+sqrt%28+9%2B180+%29%29%2F2+

x+=+%28-3+%2B-+sqrt%28+189+%29%29%2F2+

x+=+%28-3+%2B-+13.75%29%2F2+
solutions:
x+=+%28-3+%2B+13.75%29%2F2+
x+=++10.75%2F2+
x+=+5.375+
and
x+=+%28-3+-+13.75%29%2F2+
x+=++-16.75%2F2+
x+=+-8.375+

so, your solutions are:
x=5
x=-5
x+=+5.375+
x+=+-8.375+







Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

how do i solve for x: x/(x-5)-2/(x+5)=50/(x^2-25)

x%2F%28x+-+5%29+-+2%2F%28x+%2B+5%29+=+50%2F%28x%5E2+-+25%29______**Note: x+%3C%3E+5

x(x + 5) - 2(x - 5) = 50 ------ Multiplying by LCD, (x - 5)(x + 5), or x%5E2+-+25

x%5E2+%2B+5x+-+2x+%2B+10+=+50

x%5E2+%2B+3x+-+40+=+0

(x - 5)(x + 8) = 0

x = 5 (ignore as x+%3C%3E+5 as stated earlier)

highlight_green%28x+=+-+8%29

You can do the check!!

Send comments and “thank-yous” to “D” at MathMadEzy@aol.com