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

1 Answer
Oct 26, 2017

(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))