All Algebra II Resources
Simplify
Correct answer:
Explanation:
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
Simplify:
Correct answer:
Explanation:
Because the two rational expressions have the same denominator, we can simply add straight across the top. The denominator stays the same.
Therefore the answer is .
Simplify
Possible Answers:
The expression cannot be simplified.
Correct answer:
Explanation:
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.
Combine the following expression into one fraction:
Possible Answers:
The two fractions cannot be combined as they have different denominators.
Correct answer:
Explanation:
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:
What is ?
Correct answer:
Explanation:
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,
What is ?
Correct answer:
Explanation:
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:
Determine the value of .
Correct answer:
Explanation:
(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
Add:
Correct answer:
Explanation:
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
Subtract:
Correct answer:
Explanation:
First let us find a common denominator as follows:
Now we can subtract the numerators which gives us :
So the final answer is
Solve the rational equation:
Correct answer:
or