Question

1/x+4= 2/x^2+3x-4 - 1/1-x

Answer 1

Factor x^2+3x-4 first :)

Answer 2

\[\frac{ 1 }{ x \space + 4 } \space = \frac{ 2 }{ x ^{2} + x - 4 } \space - \frac{ 1 }{ 1 - x }\]

Answer 3

I guess we are asked to solve this equation for x ?

Answer 4

let's begin this problem by factoring the denominator of the 1st term on the right side of this equation:

Answer 5

\[\frac{ 1 }{ x + 4 } \space = \frac{ 2 }{ ( \space ) ( \space ) } \space - \frac{ 1 }{ 1-x }\]

Answer 6

Would you like to try factoring the quadratic, x^2 + 3x - 4?

Answer 7

yes

Answer 8

try to solve it and did not find solution?

Answer 9

Did you get the denominator factored for the quadratic part?

Answer 10

yes

Answer 11

We have for this the following:

Answer 12

\[\frac{ 1 }{ x+4 } \space = \frac{ 2 }{ (x+4) \space (x-1) } \space - \frac{ 1 }{ 1-x }\]

Answer 13

Notice that all the denominators are then contain 1 or more factors of (x+4) and (x -1)
Let's take advantage of this to multiply this equation through by (x+4)(x-1_

Answer 14

\[\left[ \frac{ 1 }{ x+4 } \space = \frac{ 2 }{ (x+4) \space (x - 1) } \space {\frac{ 1 }{ 1-x } }\right] \space ^{(x+4)} \space ^{(x-1)} \]

Answer 15

Upon multiplying each term in pink by the blue factors,
we get:

Answer 16

\[(x-1) \space = 2 \space + (x+4)\]

Answer 17

Now lets clean up the above equation:

Answer 18

\[x - 1 = x + 6\]

Answer 19

Notice that the X's now cancel and we are left with the following:

Answer 20

\[-1 = 6\]

Answer 21

This result implies that this equation does not have a solution.

Answer 22

thanks You :3

Answer 23

yw :)