Simplify (1/a+3/(3b))/(1/a-5/(2b))

Math
1a+33b1a-52b
Cancel the common factor of 3.
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Cancel the common factor.
1a+33b1a-52b
Rewrite the expression.
1a+1b1a-52b
1a+1b1a-52b
Multiply the numerator and denominator of the complex fraction by ab⋅2.
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Multiply 1a+1b1a-52b by ab⋅2ab⋅2.
ab⋅2ab⋅2⋅1a+1b1a-52b
Combine.
ab⋅2(1a+1b)ab⋅2(1a-52b)
ab⋅2(1a+1b)ab⋅2(1a-52b)
Apply the distributive property.
ab⋅21a+ab⋅21bab⋅21a+ab⋅2(-52b)
Simplify by cancelling.
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Cancel the common factor of a.
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Factor a out of ab⋅2.
a(b⋅2)1a+ab⋅21bab⋅21a+ab⋅2(-52b)
Cancel the common factor.
a(b⋅2)1a+ab⋅21bab⋅21a+ab⋅2(-52b)
Rewrite the expression.
b⋅2+ab⋅21bab⋅21a+ab⋅2(-52b)
b⋅2+ab⋅21bab⋅21a+ab⋅2(-52b)
Cancel the common factor of b.
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Factor b out of ab⋅2.
b⋅2+b(a⋅2)1bab⋅21a+ab⋅2(-52b)
Cancel the common factor.
b⋅2+b(a⋅2)1bab⋅21a+ab⋅2(-52b)
Rewrite the expression.
b⋅2+a⋅2ab⋅21a+ab⋅2(-52b)
b⋅2+a⋅2ab⋅21a+ab⋅2(-52b)
Cancel the common factor of a.
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Factor a out of ab⋅2.
b⋅2+a⋅2a(b⋅2)1a+ab⋅2(-52b)
Cancel the common factor.
b⋅2+a⋅2a(b⋅2)1a+ab⋅2(-52b)
Rewrite the expression.
b⋅2+a⋅2b⋅2+ab⋅2(-52b)
b⋅2+a⋅2b⋅2+ab⋅2(-52b)
Cancel the common factor of 2b.
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Move the leading negative in -52b into the numerator.
b⋅2+a⋅2b⋅2+ab⋅2-52b
Factor 2b out of ab⋅2.
b⋅2+a⋅2b⋅2+2⋅b(a)-52b
Cancel the common factor.
b⋅2+a⋅2b⋅2+2⋅ba-52b
Rewrite the expression.
b⋅2+a⋅2b⋅2+a⋅-5
b⋅2+a⋅2b⋅2+a⋅-5
b⋅2+a⋅2b⋅2+a⋅-5
Factor 2 out of b⋅2+a⋅2.
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Factor 2 out of b⋅2.
2⋅b+a⋅2b⋅2+a⋅-5
Factor 2 out of a⋅2.
2⋅b+2⋅ab⋅2+a⋅-5
Factor 2 out of 2⋅b+2⋅a.
2(b+a)b⋅2+a⋅-5
2(b+a)b⋅2+a⋅-5
Simplify the denominator.
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Move 2 to the left of b.
2(b+a)2⋅b+a⋅-5
Move -5 to the left of a.
2(b+a)2b-5a
2(b+a)2b-5a
Simplify (1/a+3/(3b))/(1/a-5/(2b))

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