Solve the rational equation?

Question

30/X - 30/X-1 = -1

Thanks

Answer 1

30/x - 30/(x-1) = -1
Multiply everything by x(x-1)
(30/x)x(x-1) - (30/(x-1))x(x-1) = -1x(x-1)
30(x-1) - 30(x) = -x^2 + x
30x - 30 - 30x = -x^2 + x
Move everything to the left side and cancel 30x
x^2 -x - 30 = 0
(x-6)(x+5) = 0
x - 6 = 0 or x + 5 = 0
x = 6 or x = -5

Answer 2

I'm assuming you mean 30/x - 30/(x-1) = -1, or otherwise your equation would be 0 = 0. So, we'll assume the first.

First step is to multiply the whole equation (both sides) by x-1.

[30(x-1)]/x - 30 = -(x-1)

Second step is to multiply the entire equation by x.

30(x-1) - 30x = -x(x-1)

x^2 - x - 30 = 0

(x-6)(x+5)=0

x = 6,-5

Answer 3

I assume you mean

30/x - 30/(x-1) = -1

(A reminder that brackets are important because they show that they are ALL on the bottom. If the above is not what you meant, I apologize in advance.)

In order to get rid of all fractions, you multiply both sides by
(x)(x-1). This will get rid of the fractions on the left hand side, leaving a product to be multiplied behind.

30(x-1) - 30(x) = -1(x)(x - 1)

Now, expand, to get

30x - 30 - 30x = (-1)(x^2 - x)

And expand some more

-30 = -x^2 + x

And then bring everything over to the left hand side

x^2 - x - 30 = 0

Factoring, we get

(x - 6)(x+5) = 0
Therefore, x = 6, -5

Answer 4

if you mean
(30/x) - (30/x) - 1 = -1

then the answer is:
(30/x) - (30/x) - 1 = -1
(30/x) - (30/x) = 0
30/x = 30/x
1/x = 1/x
x = x
x = all numbers

However if you mean:
(30/x) - 30/(x-1) = -1

then the answer is:
(30/x) - 30/(x-1) = -1
30*(x-1) - 30*x = -1*x*(x-1)
30x -30 -30x = -x*x + x
x^2 -x -30 = 0
(x-6)*(x+5) = 0
x = 6, -5

Answer 5

the LCD is x(x-1)
30(x-1)-30x=-1x(x-1)
30x-30-30x=-x^2+x
-30=-x^2+x
adding x^2-x
x^2-x-30=0
(x-6)(x+5)=0
x=6 or -5

Answer 6

x= 6
x= -5