Simplify. Identify any x-values for which the expression is undefined.

Question

1. (4x-8)/(x^2-2x)

2. (8x-4)/(2x^2+9x-5)

Answer 1

1.

4 x - 8 = 4 ( x - 2 )

x ^ 2 - 2 x = x ( x - 2 )

(4 x - 8 ) / ( x ^ 2 - 2 x ) =

4 ( x - 2 ) / [ x ( x - 2 ) ] =

4 / x

2.

( 8 x - 4 ) = 4 ( 2 x - 1 )

2 x ^ 2 + 9 x - 5 =

2 x ^ 2 + 9 x - 5 + x - x =

( 2 x ^ 2 - x ) + ( 10 x - 5 ) =

x ( 2 x - 1 ) + 5 ( 2 x - 1 ) =

( 2 x - 1 ) ( x + 5 )

( 8 x - 4 ) / ( 2 x ^ 2 + 9 x -5 ) =

4 ( 2 x - 1 ) / [( 2 x - 1 ) ( x + 5 ) ] =

4 / ( x + 5 ) =