# How do you use cross products to solve #3/4=x/(x+3)#?

##### 3 Answers

#### Explanation:

or

or

or

x = 9

#### Explanation:

To use cross products or

#color(blue)"cross multiplication"# as it is also named.

#color(red)(3)/color(blue)(4)=color(blue)(x)/color(red)(x+3)# now multiply the terms in

#color(blue)("blue")" and "color(red)("red")# (X) and equate them.

#rArrcolor(blue)(4x)=color(red)(3(x+3))# distribute the bracket : 4x = 3x + 9

subtract 3x from both sides to solve for x

#4x-3x=cancel(3x)+9cancel(-3x)rArrx=9#

This is why the cross product works!!!

#### Explanation:

The cross product is a shortcut that bypasses some stages in solving by first principles. I will use first principles so you can see where the shortcut takes over.

A fraction is split up into two parts. Using descriptive but

When you wish to

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Using a 'common denominator' of

If you look at the numerators you will see the result you get by the short cut

Multiply both sides by