+0

+1
282
2
+35

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
+89874
+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
+7324
+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