This is the given equation to solve:

First I simplified the denominators:

Then I multiplied the top and bottom of the first fraction by 2 and 5:

Next, I multiplied the top and bottom of the second fraction by (x-3):

Lastly, I multiplied the top and bottom of the third fraction by 5:

This gives us the same denominator on each fraction, looking like this:

By multiplying each fraction by 10x-30, we can clear the denominators:

Combining the x coefficients and adding 9 to both sides gives us:

We can conclude that x=2 since 14 divided by 7 equals 2.

However, every calculator I use says that x does not equal 2, but instead equals this:

Where did I go wrong?

Nvr2MuchPie
Oct 24, 2017

#1**+4 **

Here's the way I do it

x / [ x - 3 ] - 3/10 = 1 / [ 2 ( x - 3) ] multiply through by 2

2x / [ x - 3 ] - 6/10 = 1 / (x - 3) rearrange as

2x / [ x - 3] - 1 / [x - 3] = 6/10 reduce 6/10 to 3/5

[ 2x - 1 ] / [ x - 3 ] = 3/5 cross- multiply

5 [ 2x - 1 ] = 3 [ x - 3] simplify

10x - 5 = 3x - 9 add 5 to both sides, subtract 3x from both sides

7x = -4 divide both sides by 7

x = - 4 / 7

CPhill
Oct 24, 2017

#2**+1 **

I think the error occurs in this step and in the next step.

Here, you said + when it should be minus. It should be

\(\frac{10x}{10x-30}-\frac{3x-9}{10x-30}\,=\,\frac{5}{10x-30}\)

And then, after multiplying through by 10x - 30 , we get

10x - (3x - 9) = 5 ( Somehow in your next step, you did get the minus on the 3x . )

10x - 3x + 9 = 5

10x - 3x = 5 - 9

7x = -4

x = -4/7

hectictar
Oct 24, 2017