Question

Vrite as a single fraction. (6u)/(u^(2)-5u-14)+(4)/(u-4)-(7)/(u-7) Simplify your answer as much as possible.

Answer 1

To write the expression as a single fraction, find a common denominator for all the terms. Then expand and combine like terms to simplify the expression.

Step-by-step explanation:

To write the expression as a single fraction, we need to find a common denominator for all the terms. The common denominator will be (u-4)(u-7) since it contains all the individual denominators.

Using the common denominator, we can rewrite the expression as:

(6u(u-4)(u-7) + 4(u-7) - 7(u-4)) / ((u-4)(u-7))

Expanding the terms in the numerator gives:

(6u(u^2-11u+28) + 4u - 28 - 7u + 28) / ((u-4)(u-7))

Combining like terms in the numerator gives:

(6u^3 - 71u^2 + 132u) / ((u-4)(u-7))

This is the expression written as a single fraction, which cannot be simplified further.