Intermediate Single-Variable Algebra - Algebra II

First factor the denominators which gives us the following:

The two rational fractions have a common denominator hence they are like "like fractions". Hence we get:

Simplifying gives us

First let us find a common denominator as follows:

Now we can subtract the numerators which gives us :

So the final answer is

This is a more complicated form of

Find the least common denominator (LCD) and convert each fraction to the LCD, then add the numerators. Simplify as needed.

which is equivalent to

Simplify to get

With rational equations we must first note the domain, which is all real numbers except . (Recall, the denominator cannot equal zero. Thus, to find the domain set each denominator equal to zero and solve for what the variable cannot be.)

The least common denominator or and is . Multiply every term by the LCD to cancel out the denominators. The equation reduces to . We can FOIL to expand the equation to . Combine like terms and solve: . Factor the quadratic and set each factor equal to zero to obtain the solution, which is or . These answers are valid because they are in the domain.

(x+5)(x+3) is the common denominator for this problem making the numerators 7(x+3) and 8(x+5).

7(x+3)+8(x+5)= 7x+21+8x+40= 15x+61

A=61

a. Find a common denominator by identifying the Least Common Multiple of both denominators. The LCM of 3 and 1 is 3. The LCM of and is . Therefore, the common denominator is .

b. Write an equivialent fraction to using as the denominator. Multiply both the numerator and the denominator by to get . Notice that the second fraction in the original expression already has as a denominator, so it does not need to be converted.

The expression should now look like: .

c. Subtract the numerators, putting the difference over the common denominator.

To combine fractions of different denominators, we must first find a common denominator between the two. We can do this by multiplying the first fraction by and the second fraction by . We therefore obtain:

Since these fractions have the same denominators, we can now combine them, and our final answer is therefore:

We start by adjusting both terms to the same denominator which is 2 x 3 = 6

Then we adjust the numerators by multiplying x+1 by 2 and 2x-5 by 3

The results are:

So the final answer is,

Start by putting both equations at the same denominator.

2x+4 = (x+2) x 2 so we only need to adjust the first term:

Then we subtract the numerators, remembering to distribute the negative sign to all terms of the second fraction's numerator:

First, simplify the expression before attempting to combine like-terms.

Combine like-terms.

The values can only be added or subtracted if there are like-terms in the expression. Since there are no like-terms in the question, the question is already simplified as is. All the other answers given are incorrect.

There are multiple operations required in this problem. The exponent must be eliminated before distributing the negative sign. Use the FOIL method which means to mulitply the first terms together, then multiply the outer terms together, then multiply the inner terms togethers, and lastly, mulitply the last terms together.

The negative sign can now be distributed.

First, find the common denominator, which is . Then, make sure to offset each numerator. Multiply by y to get . Multiply by x to get . Then, combine numerators to get . Then, put the numerator over the denominator to get your answer: .

Make a common denominator:

Combine and subtract numerators:

To start this problem, you must first identify the common denominator, which in this case is teh two denominators multiplied together: . Next, offset the numerators with the newly changed denominators: . Then, add numerators to get: . Put the numerator over your denominator and check to make sure it can't be simplified anymore (it can't). Your answer is: .

To combine these rational expressions, first find the common denominator. In this case, it is . Then, offset the second equation so that you get the correct denominator: . Then, combine the numerators: . Put your numerator over the denominator for your answer: .

First find the lowest common denominator. In this case, it will be x(x+2).

Multiply each fraction to get the common denominator then solve:

To be able add or subtract the numerator, the denominators must be the same.

To get the same denominator, multiply both uncommon denominators together.

Convert both fractions to the like denominator.

For the numerator of the first term, expand the binomials.

Evaluate the numerator of the second term.

Rewrite the fractions.

To combine the numerators as one fraction, enclose the numerator of the second term in parentheses.

Simplify the numerator by distributing the negative sign and combine like-terms.

There are no similar common factors that will help reduce this expression any further.

The answer is:

In order to solve this rational expression, denominators must be common.

Multiply both denominators together.

Convert the fractions with the same base denominator. Multiply the numerator with what was multiplied on the denominator to achieve the new denominator.

Combine the two fractions into a single fraction.

Simplify the numerator on the right side.

The answer is: