Question

Solve for x
1/a+1/b+1/x=1/a+b+x
(where x is not equal to -a,-b)


Question for class10

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Answer 1

1 / a + 1 / b + 1 / x = 1 / ( a + b + x )

1 / a + 1 / b = 1 / ( a + b + x ) - 1 / x

1 / a + 1 / b = { x - ( a + b + x ) } / { ( a + b + x )x }

( a + b ) / ab = { x - a - b - x } / { ( a + b + x )x }

( a + b ) / ab = { - a - b } / { ( a + b + x ) x }

( a + b ) / ab = - ( a + b ) / { ( a + b + x )x }

1 / ab = - 1 / { ( a + b + x ) x }

( a + b + x )x = -ab

ax + bx + x^2  = - ab

x^2 + ax + bx + ab = 0

x( x + a ) + b( x + a ) = 0

x = - a or  x = - b       [ By Zero Product Rule ]

Therefore the values of x satisfying the equation is -a or -b.

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