Question

1. Simplify the expression (x/x-2)+(5/x+3). Show your work.

Answer 1

[x ÷( x -2) ] + [ 5 ÷( x +3)] =
`(x^(2)+ 8 x -10)/(x^(2) + x -6)`

Explanation:

[x ÷( x -2) ] + [ 5 ÷( x +3)]

LCM = (x -2) (x + 3)

{ x ( x+3) + 5 ( x -2)} ÷{ ( x-2) ( x +3)

i.e (x² + 3 x + 5 x - 10 ) ÷ { x² + 3 x - 2 x - 6}

i.e ( x² + 8 x - 10) ÷ ( x² + x - 6)

=
`(x^(2)+ 8 x -10)/(x^(2) + x -6)`