Question

Q.solve 150/(x-5)-150/x=1

Answer 1

$\frac{150}{x - 5 } - \frac{150}{x} = 1 \\ \\ \\ \rightarrow \frac{150x - 150( x - 5 )}{x(x - 1 ) }= 1 \\ \\ \\ \rightarrow \frac{150x - 150x + 750}{ x^2 - 5x } = 1 \\ \\ \\ \rightarrow 750 = 1 ( x^2 - 5x ) \\ \\ \\ \rightarrow x^2 - 5x - 750 = 0 \\ \\ \\ \rightarrow x^2 - ( 30 - 25 )x - 750 = 0 \\ \\ \\ \rightarrow x^2 - 30x + 25x - 750 = 0 \\ \\ \\ \rightarrow x( x - 30 ) + 25( x - 30 ) = 0 \\ \\ \\ \rightarrow ( x + 25 )( x - 30 ) = 0$

Hence, x = 30 Or -25

Answer 2

$\frac{150}{x - 5 } - \frac{150}{x} = 1 \\ \\ \\ \rightarrow \frac{150x - 150( x - 5 )}{x(x - 1 ) }= 1 \\ \\ \\ \rightarrow \frac{150x - 150x + 750}{ x^2 - 5x } = 1 \\ \\ \\ \rightarrow 750 = 1 ( x^2 - 5x ) \\ \\ \\ \rightarrow x^2 - 5x - 750 = 0 \\ \\ \\ \rightarrow x^2 - ( 30 - 25 )x - 750 = 0 \\ \\ \\ \rightarrow x^2 - 30x + 25x - 750 = 0 \\ \\ \\ \rightarrow x( x - 30 ) + 25( x - 30 ) = 0 \\ \\ \\ \rightarrow ( x + 25 )( x - 30 ) = 0$

Hence, x = 30 Or -25