Question

How do you multiply and simplify `\frac { x ^ { 2} - 3x } { x ^ { 2} - 6x + 5} \cdot \frac { x - 1} { x ^ { 2} + 2x } \div \frac { 5x } { x ^ { 2} - 7x + 10}`?

Answer 1

`(x^2-5x+6)/(5x^2+10x)`

Explanation:

`(x^2-3x)/(x^2-6x+5)*(x-1)/(x^2+2x)/[(5x)/(x^2-7x+10)]`

=`(x^2-3x)/(x^2-6x+5)(x-1)/(x^2+2x)(x^2-7x+10)/(5x)`

=`(x(x-3))/[(x-1)(x-5)]*(x-1)/(x(x+2))` `(x^2-7x+10)/(5x)`

=`(x-3)/[(x-5)(x+2)]` `((x-2)(x-5))/(5x)`

=`[(x-3)(x-2)]/[5x(x+2)]`

=`(x^2-5x+6)/(5x^2+10x)`