Question

How do you evaluate `\frac { 15x ^ { 2} - 12x } { 36x + 45} \times \frac { 24x + 30} { 15x ^ { 2} + 3x - 12}`?

Answer 1

`(15x^2-12x)/(36x+45) * (24x+30)/(15x^2+3x-12)`

factorise:

`15x^2-12x = 3x(5x-4)`

`36x+45 = 9(4x+5)`

`24x+30 = 6(4x+5)`

`15x^2+3x-12 = 3(5x^2+x-4)`

cross-cancel:

`(cancel3x(5x-4))/(cancel9 3(4x+5)) * (cancel6 2(4x+5))/(cancel3(5x^2+x+4))`

`= (x(5x-4))/(3(4x+5)) * (2(4x+5))/((5x^2+x-4))`

`5x^2+x-4 = (5x-4)(x+1)`

`(x(5x-4))/(3(4x+5)) * (2(4x+5))/((5x-4)(x+1)`

`=(xcancel((5x-4)))/(3cancel((4x+5))) * (2cancel((4x+5)))/(cancel((5x-4))(x+1)`

`=x/3 * 2/(x+1)`

`=(2x)/(3(x+1))`