adding and subtracting expressions
Answers
Answer:
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)