Solve following equation.?

Question

x /(2x-8) + 16/(x^2 -16) = 1/2

Answer 1

Your first step is to factor the denominators. The reason why you're doing this is to determine what the best number to multiply both sides with is, to eliminate all fractions.

x/[2(x-4)] + 16[(x-4)(x+4)] = 1/2

Note that the best number to multiply everything by would be 2(x-4)(x+4). This will eliminate all fractions, but be sure to make yourself aware of what stays behind as a result of doing so. All you have to do is multiply what's missing in the denominator.

x(x+4) + 16(2) = (x-4)(x+4)

Now, we expand everything.

x^2 + 4x + 32 = x^2 - 16

And then group like terms. The x^2 terms should cancel each other out. Let's move everything to the left hand side.

4x + 32 + 16 = 0
4x + 48 = 0
4x = -48
x = -12

Answer 2

x /(2x-8) + 16/(x^2 -16) = 1/2
x + 16(2x-8)/(x^2 -16) = 1/2(2x-8)
x + [32(x-4)]/[(x+4)(x-4)]= x-4
x + 32/(x+4) = x-4
x(x+4) + 32 = (x-4)(x+4)
x² + 4x +32 = x² -16
4x = -48
x = -12

Answer 3

To add fractions: you multiply the denomenators together, then multiply each numerator by the denomenator of the other fraction
So: (2x-8)(x^2 -16) on the bottom, & x(x^2 -16) & 16(2x-8) on top
Equals: 16x(x^2 -16)(2x-8) / (2x-8)(x^2 -16)
Cancelling out leaves you with: 16x
So: 16x= 1/2
Therefore: x= 1/32 or 0.03125

Answer 4

x/2(x-4) + 16/{(x+4)(x-4)} = 1/2
(x^2 + 4x + 32)/2(x^2 - 16) = 1/2
x^2 + 4x + 32 = x^2 - 16
4x = -48
x = -12

Warning !!! = The other three have slight mistakes!!!
I have given them low ratings for you.

Answer 5

Multiply each side by both x-4 and x-8 and simplify.

Answer 6

approach A: 5X = one hundred and fifty 5 5 x X = one hundred and fifty 5 X = one hundred and fifty 5/5 X = 31 OR approach B: 5X = one hundred and fifty 5 5 x X = one hundred and fifty 5 5 = one hundred and fifty 5/X X = one hundred and fifty 5/5 X = 31 the suitable approach is extra accessible, even with the undeniable fact that the bottom is likewise in theory perfect. In tests, the suitable approach is the perfect to apply. wish this facilitates!

Answer 7

[x/2(x-4)]+[16/(x+4)(x-4)=1/2
multiplying by 2(x-4)(x+4)
=x(x+4)+32=x^2-16
4x+48=0
4x=-48
x=-12