3/x-1-2/x-2=1/x-3
please answer step by step
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Answer:
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1
Combine multiplied terms into a single fraction
3
−
1
−
1
⋅
2
−
2
=
1
−
3
3
x
−
1
−
1
⋅
2
x
−
2
=
1
x
−
3
x3−1−1⋅x2−2=x1−3
3
−
1
+
−
1
⋅
2
−
2
=
1
−
3
3
x
−
1
+
−
1
⋅
2
x
−
2
=
1
x
−
3
x3−1+x−1⋅2−2=x1−3
2
Multiply the numbers
3
−
1
+
−
1
⋅
2
−
2
=
1
−
3
3
x
−
1
+
−
1
⋅
2
x
−
2
=
1
x
−
3
x3−1+x−1⋅2−2=x1−3
3
−
1
+
−
2
−
2
=
1
−
3
3
x
−
1
+
−
2
x
−
2
=
1
x
−
3
x3−1+x−2−2=x1−3
3
Subtract the numbers
3
−
1
+
−
2
−
2
=
1
−
3
3
x
−
1
+
−
2
x
−
2
=
1
x
−
3
x3−1+x−2−2=x1−3
3
−
3
+
−
2
=
1
−
3
3
x
−
3
+
−
2
x
=
1
x
−
3
x3−3+x−2=x1−3
4
Add
3
3
3
to both sides of the equation
3
−
3
+
−
2
=
1
−
3
3
x
−
3
+
−
2
x
=
1
x
−
3
x3−3+x−2=x1−3
3
−
3
+
−
2
+
3
=
1
−
3
+
3
3
x
−
3
+
−
2
x
+
3
=
1
x
−
3
+
3
x3−3+x−2+3=x1−3+3
5
Simplify
Add the numbers
Add the numbers
3
+
−
2
=
1
3
x
+
−
2
x
=
1
x
x3+x−2=x1
6
Multiply all terms by the same value to eliminate fraction denominators
3
+
−
2
=
1
3
x
+
−
2
x
=
1
x
x3+x−2=x1
(
3
+
−
2
)
=
⋅
1
x
(
3
x
+
−
2
x
)
=
x
⋅
1
x
x(x3+x−2)=x⋅x1
7
Simplify
Distribute
Cancel multiplied terms that are in the denominator
Cancel multiplied terms that are in the denominator
Subtract the numbers
Cancel multiplied terms that are in the denominator
1
3
−
1
−
1
⋅
2
−
2
=
1
−
3
3
x
−
1
−
1
⋅
2
x
−
2
=
1
x
−
3
x3−1−1⋅x2−2=x1−3
3
−
1
+
−
1
⋅
2
−
2
=
1
−
3
3
x
−
1
+
−
1
⋅
2
x
−
2
=
1
x
−
3
x3−1+x−1⋅2−2=x1−3
2
Multiply the numbers
3
−
1
+
−
1
⋅
2
−
2
=
1
−
3
3
x
−
1
+
−
1
⋅
2
x
−
2
=
1
x
−
3
x3−1+x−1⋅2−2=x1−3
3
−
1
+
−
2
−
2
=
1
−
3
3
x
−
1
+
−
2
x
−
2
=
1
x
−
3
x3−1+x−2−2=x1−3
3
Subtract the numbers
3
−
1
+
−
2
−
2
=
1
−
3
3
x
−
1
+
−
2
x
−
2
=
1
x
−
3
x3−1+x−2−2=x1−3
3
−
3
+
−
2
=
1
−
3
3
x
−
3
+
−
2
x
=
1
x
−
3
x3−3+x−2=x1−3
4
Add
3
3
3
to both sides of the equation
3
−
3
+
−
2
=
1
−
3
3
x
−
3
+
−
2
x
=
1
x
−
3
x3−3+x−2=x1−3
3
−
3
+
−
2
+
3
=
1
−
3
+
3
3
x
−
3
+
−
2
x
+
3
=
1
x
−
3
+
3
x3−3+x−2+3=x1−3+3
5
Simplify
Add the numbers
Add the numbers
3
+
−
2
=
1
3
x
+
−
2
x
=
1
x
x3+x−2=x1
6
Multiply all terms by the same value to eliminate fraction denominators
3
+
−
2
=
1
3
x
+
−
2
x
=
1
x
x3+x−2=x1
(
3
+
−
2
)
=
⋅
1
x
(
3
x
+
−
2
x
)
=
x
⋅
1
x
x(x3+x−2)=x⋅x1
7
Simplify
Distribute
Cancel multiplied terms that are in the denominator
Cancel multiplied terms that are in the denominator
Subtract the numbers
Cancel multiplied terms that are in the denominator
1
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