algebra help?

Question

(x+1)/(x-1)=(-12/x+3)+(8/x^2+2x-3)


I'm sure theres a simple thing I'm missing but I can't figure out how to solve this.

it looks like it cut off the last part, its :x^2+2x-3

Answer 1

Original equation:
(x+1) / (x-1) = ( -12 / (x+3) ) + ( 8 / x^2+2x-3 )

Now factor the x^2 + 2x - 3:
(x+1) / (x-1) = ( -12 / (x+3) ) + ( 8 / (x + 3)(x - 1) )

Multiply both sides by (x-1): (x cannot be 1)
(x+1) = ( -12 ( x -1 ) / ( x+3 ) ) + ( 8 / (x + 3) )

Multiply both sides by (x+3): (x cannot be -3)
(x+1)(x+3) = -12 ( x -1 ) + 8

Now simplify the right side:
(x+1)(x+3) = -12x + 12 + 8
(x+1)(x+3) = -12x + 20

Multiply through:
(x^2 + 4x + 3) = -12x + 20

Add 12x to both sides:
x^2 + 16x + 3 = 20

Subtract 20 from both sides:
x^2 + 16x -17 = 0

Now factor the left side:
(x + 17)(x - 1) = 0

That would imply answers of x = -17 and x = 1, but we already eliminated x = 1 as an option (since it would make a 0 denominator).

So the answer is x = -17.

You should double check this answer, by substituting into the original equation:
(x+1) / (x-1) = ( -12 / (x+3) ) + ( 8 / x^2+2x-3 )
((-17)+1) / ((-17)-1) = ( -12 / ((-17)+3) ) + ( 8 / (-17)^2+2(-17)-3 )
-16 / -18 = -12 / -14 + 8 / (-17)^2 - 34 - 3
8 / 9 = 6 / 7 + 8 / (289 - 37)
8 / 9 = 6 / 7 + 8 / 252
8 / 9 = 6 / 7 + 2 / 63
56 / 63 = 54 / 63 + 2 / 64
56 = 54 + 2
56 = 56 (check!)

That was rather complicated, I'd say. The key was to factor the denominator and multiply through to get just the numerators. Then it is much simpler to solve.

Anyway, the answer is x = -17

Answer 2

(x+1) / (x-1) = ( -12 / (x+3) ) + ( 8 / x^2+2x-3 )

multiply both sides by x^2+2x-3=(x-1)*(x+3)

you get

(x+1)*(x+3) = -12*(x-1) +8

x^2 + 4x + 3 = -12x +12 +8

x^2 + 16X - 17 = 0

X= -17

Answer 3

(x+1)(x+3)/((x-1)(x+3)) = (-12(x-1)+8)/((x+3)(x-1))
for x not equal 1 or -3

(x+1)(x+3) = -12x+20

x^2 +16x-17 = 0

(x+17)(x-1) = 0 . Therefore x = -17 [x=1 is already excluded]

Answer 4

You must put more spaces in your equation or it looks like this.
(x+1)/(x-1)=(-12/x+3)+(8/x^2+2...

Answer 5

For increasing cubic binomials the standard formula is as follows: (a + b) ^ 3 = a^3 + 3*a^2*b^a million + 3*a^a million*b^2 + b^3 on your case, a is x and b is -y^5 So (x - y^5)^3 = x^3 + 3*x^2*(-y^5)^a million + 3*x^a million*(-y^5)^2 + (-y^5)^3 Simplified: =x^3 - 3x^2*y^5 + 3x*y^10 - y^15 :D