To get rid of a fraction, we multiply by the reciprocal. So we take and multiply both sides by :

and cancel each other out, so we are left with or .

To solve for we must get all of the numbers on the other side of the equation of .

To do this in a problem where a number is being added to , we must subtract the number from both sides of the equation.

In this case the number is so we subtract from each side of the equation to make it look like this

To subtract fractions we must first ensure that we have the same denominator which is the bottom part of the fraction.

To do this we must find the least common multiple of the denominators.

The least common multiple is the smallest number that multiples of both of the denominators multiply to.

In this case the LCM is

We then multiply the numerator and denominator of by to get the same denominator because anything divided by itself is one so the fractions maintain their same value as the numbers change into the format we need to determine the answer.

To multiply a fraction you multiply the top number of the first fraction by the top number of the second fraction and the bottom number of the first fraction by the bottom number of the second fraction so it would look like this

After doing this we then subtract the first numerator (top part of the fraction) from the second numerator and place the result over the new denominator

The final answer is

To solve for , the first thing we need to do is isolate the variable. That means we want ONLY on the left side of the equation.

To divide by a fraction, we need to multiply by the reciprocal. The reciprocal of .

To get rid of a fraction, we multiply by the reciprocal. So we take and multiply both sides by :

Notice that and cancel out, leaving us with .

At this point, you can either plug into your calculator, or you can solve this in pieces.

We can do some manipulation to get:

, so we can plug that into .

To get rid of a fraction, we multiply by the reciprocal, so we take and multiply both sides by :

Since , we can simplify that equation to .

Therefore, .

When solving for , we want to isolate it. That means we want only on the right side of the equation.

For our given equation, , we need to divide both sides by .

Dividing by a fraction is the same as multiplying by the reciprocal so this will look like:

To get rid of a fraction, we multiply by the reciprocal. So we take and multiply both sides by :

Since , we can simplify that equation to .

Therefore, .

Multiply both sides of the equation by .

We can check our answer by plugging it back into the equation.

We know that our answer works.