solve
3/x-1 - 2/x-2 = 1 / x-3
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Answers
Answered by
3
Step-by-step explanation:
Factorise the denominator of the last term by inspection:
3
x
−
2
=
1
x
−
1
+
7
(
x
−
2
)
(
x
−
1
)
We need to get the
x
's off the denominator to solve. I see lots of common terms, so to get rid of them, multiply both sides of the equation by
(
x
−
2
)
(
x
−
1
)
:
3
(
x
−
2
)
(
x
−
1
)
x
−
2
=
1
(
x
−
2
)
(
x
−
1
)
x
−
1
+
7
(
x
−
2
)
(
x
−
1
)
(
x
−
2
)
(
x
−
1
)
Now we can cancel out a whole bunch of terms:
3
x
−
2
(
x
−
1
)
x
−
2
=
1
(
x
−
2
)
x
−
1
x
−
1
+
7
x
−
2
x
−
1
x
−
2
x
−
1
And we are left with this:
3
(
x
−
1
)
=
(
x
−
2
)
+
7
Expand the brackets, and put all the
x
terms on the left, and the constants on the right:
3
x
−
3
=
x
+
5
2
x
=
8
Answered by
1
I hope it is clear
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