An algebra problem by Ali Bahramishad

Algebra Level 2

Find the value for x:

x/a-x/b=a-b

ab -ab -2ab a/b

Ali Bahramishad by Ali Bahramishad , 21, Iran

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2 solutions

Michael Fuller
May 18, 2015

x a − x b = a − b x b a b − x a b a = a − b x ( b − a ) a b = a − b x ( b − a ) = a b ( a − b ) x = a b ( a − b ) ( b − a ) x = a b × − ( b − a ) ( b − a ) x = a b × − 1 x = − a b \frac { x }{ a } -\frac { x }{ b } =a-b\\ \frac { xb }{ ab } -\frac { xa }{ ba } =a-b\\ \frac { x(b-a) }{ ab } =a-b\\ x(b-a)=ab(a-b)\\ x=\frac { ab(a-b) }{ (b-a) } \\ x=ab\times \frac { -(b-a) }{ (b-a) } \\ x=ab\times -1\\ x=\boxed { -ab }

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Good one:)

Ali Bahramishad - 6 years ago
Ali Bahramishad
May 5, 2015

(bx-ax)/ab=a-b -> (b-a)x=-ab(b-a) -> x=-ab

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