# How do you solve #3/5=12/(x+8)#?

##### 1 Answer

#### Explanation:

Two fractions are equal if the product of the numerator of first and the denominator of the second is **equal** to the product of the denominator of the first and the numerator of the second.

In other words, if you **cross-multiply** the numerators and denominators of the two fractions and end up with the same product, you can say that the two fractions are **equal**.

In this case, you have

#color(blue)(3)/color(purple)(5) = color(blue)(12)/color(purple)(x+8)#

Multiply the numerator of the first fraction by the denominator of the second fraction

#color(blue)(3) xx (color(purple)(x+8)) = 3x + 24#

Multiply the denominator of the first fraction and the numerator of the second fraction

#color(purple)(5) xx color(blue)(12) = 60#

The two fractions are equal if

#3x + 24 = 60#

Solve for

#3x = 60 - 24#

#x = (60-24)/3 = 12#

Do a quick check to make sure that the calculations are correct

#3/5 = 12/(12 + 8)#

#3/5 = 12/20#

#3/5 = (color(red)(cancel(color(black)(4))) xx 3)/(color(red)(cancel(color(black)(4))) xx 5)" "color(green)(sqrt())#