Step by step
The question
Question: solve 10/(x − 1) − 2 = 6/(x − 1).
First: a bottom can never be 0.
x = 1 makes x − 1 0.
So x ≠ 1.
1 Remove the fractions
The bottom is (x − 1).
Times (x − 1) will remove it.
We multiply every part by (x − 1).
We do it on both sides, so they stay equal.
(x − 1) divided by (x − 1) is 1.
(x − 1) times 2 is 2(x − 1).
(x − 1) divided by (x − 1) is 1.
Write what is left.
No more fractions!
2 Open the brackets
The −2 in front of the bracket multiplies every part inside.
So we write −2 times each part.
Work out each multiplication.
3 Group like terms
Terms are the parts between the + and − signs.
Like terms are the same kind: same letters, same powers.
Plain numbers go together.
10 + 2 = 12.
Now we have 12 − 2x = 6.
We want x by itself.
Two things are stuck to x: times −2 and + 12.
The + 12 is on the outside, so it comes off first.
Then the times −2.
4 Remove the 12
To remove 12, we take away 12.
We do it on both sides, so they stay equal.
12 and − 12 make zero.
Cross them out.
6 − 12 = −6.
Now we have −2x = −6.
5 Remove the −2
−2x means −2 times x.
We want just x.
To remove times −2, we divide by −2.
We do it on both sides, so they stay equal.
−2 divided by −2 is 1.
So just x is left.
−6 divided by −2 is 3.
So x = 3!
6 Check
Let's check: put 3 in place of x.
First the left side.
Now the right side.
Both sides are 3.
So x = 3 is right!
Let's look back.
First: remove the fractions.
Then: open the brackets.
Then: group like terms.
Then: remove the 12.
Then: remove the −2.
Last: check.