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Rational Expressions - Add/Subtract - Part 1 - How it Works - Video
Rational Expressions - Add/Subtract - Part 1 - How it Works - Video
Example 1
Example 1
Example 1:
Here we have two proper fractions 1/4 and 2/5. In this question we want to add them together. First, we must find a common denominator. One method is list the multiples of 4: 4, 8, 12, 16, and 20. Then list the multiple of 5: 5, 10, 15, and 20. Lucky for us the common denominator is early, and it is 20 in this case. But, sometimes, it is not, which leads us to method two.
In method 2 we are going to multiply the denominator in the first fraction, 1/4, which is 4, by the denominator of the second fraction, 2/5, which is 5, and the result of 4 * 5 is 20.
Both give the same result that will help us with the rational expressions.
1/4 + 2/5
(5/5) * (1/4) + (2/5) * (4/4)
5(1) / 5(4) + 2(4) / 5(4)
[ 5(1) + 2(4) ] / 5(4)
[ 5 + 8 ] / 20
13 / 20
Given
Multiply each fraction by 1 (5/5 or 4/4) to get common denominator
Get rid of the multiplication signs
Combine fractions
Multiply
Combine like terms
Example 2
Example 2
Example 2:
Here we have 3 / [ 5x ] - 4 / 5.
Let's find the factors of 5x and 5. The factors of 5x are 5 and x. 5 only has one factor that we need to worry about, which is 5.
So 5x has two different factors and 5 only has one different factor. We need the two denominators to match so that we can combine the numerators. So we have to multiply the fraction on the right by x so that both fractions have 5x.
3 / [5x] - 4 / 5
3 / [5x] - (4 / 5) * (x/x)
3 / [5x] - (4x) / [5x]
(3 - 4x) / [5x]
Given
Multiply the right fraction by 1 (x/x) to get a common denominator
Get rid of the multiplication signs
Combine fraction
Example 3
Example 3
Example 3:
Here we have 5 / [4x2 - 8x] + 7 / [4x].
Let's find the factors of 4x2 - 8x and 4x. The factors of 4x2 - 8x are 4, x, and (x - 2). 4x has two factors: 4 and x.
So 4x2 - 8x has three different factors and 4x has two different factors. We need the two denominators to match so that we can combine the numerators. So we have to multiply the fraction on the right by (x - 2) so that both fractions have 4(x)(x - 2).
5 / [4x2 - 8x] + 7 / [4x]
5 / [ 4(x)(x - 2) ] + 7 / [ 4(x) ] * ( [x - 2] ) / [x - 2] )
5 / [ 4(x)(x - 2) ] + 7(x - 2) / [ 4(x)(x - 2) ]
[ 5 + 7(x - 2) ] / [ 4(x)(x - 2) ]
[5 + 7x - 14] / [ 4(x)(x - 2) ]
[7x - 9] / [ 4(x)(x - 2) ]
Given
Multiply the right fraction by 1 (x/x) to get a common denominator
Get rid of the multiplication signs
Combine fraction
Distribute 7 to the binomial
Combine like terms
Example 4
Example 4
Example 4:
Here we have 4 / (x - 4) - 5 / (x + 3).
Let's find the factors of (x - 4) and (x + 3). The factors of (x - 4) and (x + 3) are (x - 4) and (x + 3). In this case we did not have to factor but we still don't have a common denominator.
We need the two denominators to match so that we can combine the numerators. So we have to multiply the fraction on the left by (x + 3) and the fraction on the right by (x - 4) so that both fractions have (x - 4)(x + 3).
4 / (x - 4) - 5 / (x + 3)
( [x + 3] ) / [x + 3] ) * 4 / (x - 4) - 5 / (x + 3) * ( [x - 4] ) / [x - 4] )
[ 4(x + 3) ] / [ (x - 4)(x + 3) ] - [ 5(x - 4) ] / [ (x + 3)(x - 4) ]
[ 4(x + 3) - 5(x - 4) ] / [ (x + 3)(x - 4) ]
[4x + 12 - 5x + 20] / [ (x + 3)(x - 4) ]
[-x + 32] / [ (x + 3)(x - 4) ]
Given
Multiply the right fraction by 1 (x/x) to get a common denominator
Get rid of the multiplication signs
Combine fraction
Distribute 4 to the binomial and the -5 to the other
Combine like terms
Live Worksheet
Live Worksheet
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