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3. How will you subtract rational numbers in fraction form with different denominator and different signs? Give an example of subtracting rational numbers in fraction form with different denominator and different signs. ________________________________________________________ ________________________________________________________ ________________________________________________________
3. How will you subtract rational numbers in fraction form with different denominator and different signs? Give an example of subtracting rational numbers in fraction form with different denominator and different signs. ________________________________________________________ ________________________________________________________ ________________________________________________________
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Answer:
Adding and Subtracting Rational Expressions with Unlike Denominators
There are a few steps to follow when you add or subtract rational expressions with unlike denominators.
To add or subtract rational expressions with unlike denominators, first find the LCM of the denominator. The LCM of the denominators of fraction or rational expressions is also called least common denominator , or LCD.
Write each expression using the LCD. Make sure each term has the LCD as its denominator.
Add or subtract the numerators.
Simplify as needed.
Example 1:
Add 13a+14b .
Since the denominators are not the same, find the LCD.
Since 3a and 4b have no common factors, the LCM is simply their product: 3a⋅4b .
That is, the LCD of the fractions is 12ab .
Rewrite the fractions using the LCD.
(13a⋅4b4b)+(14b⋅3a3a)=4b12ab+3a12ab =3a+4b12ab
Example 2:
Add 14x2+56xy2 .
Since the denominators are not the same, find the LCD.
Here, the GCF of 4x2 and 6xy2 is 2x . So, the LCM is the product divided by 2x :
LCM=4x2⋅6xy22x =2⋅2⋅x⋅x⋅6xy22⋅x =12x2y2
Rewrite the fractions using the LCD.
14x2⋅3xy23xy2+56xy2⋅2x2x=3xy212x2y2+10x12x2y2 =3xy2+10x12x2+y2
Example 3:
Subtract 2a−3a−5 .
Since the denominators are not the same, find the LCD.
The LCM of a and a−5 is a(a−5) .
That is, the LCD of the fractions is a(a−5) .
Rewrite the fraction using the LCD.
2a−3a−5=2(a−5)a(a−5)−3aa(a−5)
Simplify the numerator.
=2a−10a(a−5)−3aa(a−5)
Subtract the numerators.
=2a−10−3aa(a−5)
Simplify.
=−a−10a(a−5)
Example 4:
Add 5c+2+6c−3 .
Since the denominators are not the same, find the LCD.
The LCM of c+2 and c−3 is (c+2)(c−3) .
That is, the LCD of the fractions is (c+2)(c−3) .
Rewrite the fraction using the LCD.
5c+2+6c−3=5(c−3)(c+2)(c−3)+6(c+2)(c+2)(c−3)
Simplify each numerator.
=5c−15(c+2)(c−3)+6c+12(c+2)(c−3)
Add the numerators.
=5c−15+6c+12(c+2)(c−3)
Simplify.
=11c−3(c+2)(c−3)
Step-by-step explanation:
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