Add.
start fraction 5 c over 2 c plus 7 end fraction plus start fraction c minus 28 over 2 c plus 7 end fraction
A. start fraction 6 c plus 28 over 4 c plus 14 end fraction
B. start fraction 6 c minus 28 over 4 c plus 14 end fraction
C. start fraction 6 c minus 28 over 2 c plus 7 end fraction
D. start fraction 4 c minus 28 over 2 c plus 7 end fraction
Simplifying each fraction by finding a common denominator of 2c + 7, we have:
start fraction 5c(2c-7) over (2c+7)(2c-7) end fraction + start fraction c-28 over 2c+7 end fraction
= start fraction (10c^2 - 35c) / (2c+7)(2c-7) end fraction + start fraction c-28 over 2c+7 end fraction
Combining the two fractions by finding a common denominator of (2c+7)(2c-7), we have:
start fraction (10c^2 - 35c + (c-28)(2c-7)) / (2c+7)(2c-7) end fraction
Simplifying the numerator, we get:
start fraction (10c^2 - 35c + 2c^2 - 49c + 196) / (2c+7)(2c-7) end fraction
= start fraction (12c^2 - 84c + 196) / (2c+7)(2c-7) end fraction
= start fraction 6(c-7) / (2c+7) end fraction
Therefore, the answer is C. start fraction 6 c - 28 over 2 c + 7 end fraction.
Subtract.
start fraction 3 n plus 2 over n plus 4 end fraction minus start fraction n minus 6 over n plus 4 end fraction
A. 2 n plus 8
B. start fraction 2 n minus 4 over n plus 4 end fraction
C. start fraction 2 n minus 8 over n plus 4 end fraction
D. 2
Using the common denominator of n + 4, we have:
start fraction (3n+2) - (n-6) over n+4 end fraction
= start fraction 3n+2 - n + 6 over n+4 end fraction
= start fraction 2n+8 over n+4 end fraction
Therefore, the answer is A. 2n+8.
Find the LCD of the pair of expressions.
one half; Start Fraction 4 over x squared End Fraction
A. 4 x squared
B. 2 x squared
C. 2 x
D. x squared
The prime factorization of the denominator of the fraction 4/x^2 is x^2, so the LCD of the two expressions is x^2.
Therefore, the answer is D. x^2.
Find the LCD of the pair of expressions.
Start Fraction 8 over 5 b End Fraction; Start Fraction 12 over 7 b-cubed c End Fraction
A. 7 b cubed c
B. 12 b cubed c squared
C. 35 b cubed c squared
D. Start Fraction a minus b + 2 over a b c cubed End Fraction
The prime factorization of the denominators are:
- 8/5b has a denominator of 5b.
- 12/7b^3c has a denominator of 7b^3c.
The LCD must include all the factors in both denominators, with the highest exponent of each factor included. Therefore, the LCD is 35b^3c.
Therefore, the answer is C. 35 b cubed c squared.
Find the LCD of the pair of expressions.
start fraction 3 m over m plus n end fraction; start fraction 3 n over m minus n end fraction
A. Left parenthesis m plus n right parenthesis times left parenthesis m minus n right parenthesis
B. 2 m
C. 2 m n
D. left parenthesis m minus n right parenthesis squared
The prime factorization of the denominators is:
- m + n
- m - n
Since these expressions have no common factors, the LCD is the product of the two denominators, which is:
(m + n)(m - n)
Therefore, the answer is A. (m + n) times (m - n).
Add.
start fraction 7 over 3 a end fraction plus 2 fifths
A. start fraction 35 plus 6 a over 3 a plus 5 end fraction
B. start fraction 35 plus 6 a over 15 a end fraction
C. start fraction 7 plus 6 a over 30 a end fraction
D. start fraction 35 plus 6 a over 30 a end fraction