You can put this solution on YOUR website! Equations in this form [fractions on both sides] are called proportions. You can convert a proportion
to a more conventional equation form by multiplying the numerator on one side by the denominator
on the other side. If you to that for both numerators, you get two products and you separate the
two products by an equal sign. Then just solve the resulting equation using algebraic
procedures. Let's apply this method to your problem.
.
Begin by multiplying the numerator by the denominator from the other side. The
resulting distributed multiplication results in the product .
.
Next multiply the numerator on the right side by the denominator on the left side. The
resulting product is .
.
Separate these two products with an equal sign and you have:
.
.
Get this in conventional quadratic form by subtracting from both sides to get:
.
.
Factor the left side of this equation to get:
.
.
Notice that this equation will be true if either of the factors on the left side equal zero
because multiplying by a zero on the left side will make the entire left side equal to
zero and therefore equal to the right side. To find the values of t that will make a factor
equal to zero, just set the two factors equal to zero (one factor at a time) and solve for t.
.
First:
.
.
Add 6 to both sides and this becomes:
.
.
Next:
.
.
Subtract 2 from both sides and this becomes:
.
.
So the two answers to this problem are and
.
You can check these answers by substituting them one at a time into the original equation you
were given and then working out the answers to make sure the left side of the equation does
in fact equal the right side. For example, let's check to see if the given equation is
equal on both sides when t is equal to +6. The original equation is:
.
.
Replace t with +6 and this equation becomes:
.
.
The denominator on the right side multiplies out to give 12 + 6 = 18 and this makes the
equation reduce to:
.
.
Notice that both sides reduce to so the equation is true when t = 6.
.
If you try the same check by substituting -2 for t you will find that is also works out such
that both sides are equal. So both answers check.
.
Hope this helps you to understand the problem and how you can start to work out proportions by
using cross multiplication to get them into a more conventional form.
.
(