Express the following expression as a single fraction with no common factors in the numerator and denominator.

Question

Express the following expression as a single fraction with no common factors in the numerator and denominator. ​  ​

Quizplus · Accepted Answer

To simplify the expression, we need to find the common denominator by finding the least common multiple of the two denominators: $4x(x+1)(x+4)$ and $7x(x+4)$. The least common multiple is $28x(x+1)(x+4)$.

We can then rewrite each fraction using the common denominator:

$$\frac{7}{7x(x+4)}-\frac{3}{4x(x+1)(x+4)}=\frac{4}{4\cdot7x(x+4)}\cdot\frac{7}{7}-\frac{7}{4\cdot7x(x+4)}\cdot\frac{3}{x+1}$$

Simplifying the expression, we get:

$$\frac{28}{28x(x+4)}-\frac{21}{28x(x+1)(x+4)}=\frac{28-21(x+1)}{28x(x+1)(x+4)}=\frac{11-21x}{28x(x+1)(x+4)}$$

Since there are no common factors in the numerator and denominator, the final answer is:

$$\frac{11-21x}{28x(x+1)(x+4)}$$

Therefore, the correct choice is (C).

Express the Following Expression as a Single Fraction with No