Add or subtract. Then simplify. If a denominator has two or more factors (other than monomials), leave it in factored form. Express the answer using the denominator of the first fraction when applicable.
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Question

Quizplus · Accepted Answer

We need to add or subtract the fractions, but they have different denominators. To get a common denominator, we need to factor the denominators and find the least common multiple.

Factorizing the denominators: 
25b^2c^2d and 4b^2c

The prime factorization of 25b^2c^2d is 5^2 * b^2 * c^2 * d
The prime factorization of 4b^2c is 2^2 * b^2 * c

The least common multiple must include all the unique prime factors raised to their highest exponent:

LCM = 2^2 * 5^2 * b^2 * c^2 * d = 500b^2c^2d

Now we need to write equivalent fractions with this common denominator:
3/25b^2c^2d - 1/4b^2c = [3*4]/[25b^2c^2d*4] - [1*(25d)]/[4b^2c*(25d)]

= 12/100b^2c^2d - 25d/100b^2c^2d

= (12-25d)/100b^2c^2d

Simplifying this expression gives us the third option: 
11ebbb8f_b971_0053_bcf2_a3a2d36d6a16_TB8306_11.

Add or Subtract