How do you simplify #(7d^2 - 14d)/(8h^5) * (12h^3)/(21d^2h - 28dh^2)#?

1 Answer
Jul 23, 2015

Answer:

Here's how you could simplify this expression.

Explanation:

Your starting expression looks like this

#(7d^2 - 14d)/(8h^5) * (12h^3)/(21d^2h - 28dh^2)#

If you take into account the fact that

#color(blue)(a/b) * color(green)(c/d) = (color(blue)(a) * color(green)(c))/(color(blue)(b) * color(green)(d)) = (color(green)(c) * color(blue)(a))/(color(blue)(b) * color(green)(d)) = color(green)(c)/color(blue)(b) * color(blue)(a)/color(green)(d)#

you can play around with this expression a little to get

#(stackrel(color(red)(3))(cancel(12))cancel(h^3))/(stackrel(color(red)(2))(cancel(8))h^cancel(5)) * (7d^2 - 14d)/(21d^2h - 28dh^2) = 3/(2h^2) * (7d^2 - 14d)/(21d^2h - 28dh^2)#

Now take a look at the second fraction. You can write

#7d^2 - 14d = 7d * (d - 2)#

and

#21d^2h - 28dh^2 = 7d * h(3d - 4h)#

Dividing these two expressions will get you

#(cancel(7d) * (d-2))/(cancel(7d) * h(3d - 4h)) = (d-2)/(h(3d - 4h))#

The overall expression now becomes

#3/(2h^2) * (d-2)/(h(3d - 4h)) = color(green)((3(d-2))/(2h^3(3d - 4h))#