Question

4/x-8 + x+2/x²-64 - 3/x²+8x

Answer 1

4/х-8+х+2/х2-64-3/х2+8х=2/х2-3/х2+8х+х-64-8+4/х=4/х-1/х2+9х-72=4х-1/х2+9х-72

Answer 2

To simplify the expression, we need to find a common denominator for all the terms. The common denominator will be (x^2 - 64), which factors to (x + 8)(x - 8). The expression can then be rewritten with the common denominator as follows:

4/(x - 8) + (x + 2)/(x^2 - 64) - 3/(x^2 + 8x)

Now, let's simplify each term and combine them:

1. Simplify 4/(x - 8): To get the common denominator, multiply both the numerator and denominator by (x + 8):

4/(x - 8) * (x + 8)/(x + 8) = 4(x + 8)/(x^2 - 64)

2. Simplify (x + 2)/(x^2 - 64): Already in its simplified form.

3. Simplify 3/(x^2 + 8x): To get the common denominator, multiply both the numerator and denominator by (x - 8):

3/(x^2 + 8x) * (x - 8)/(x - 8) = 3(x - 8)/(x^2 - 64)

Now, the simplified expression becomes:

(4(x + 8) + (x + 2) - 3(x - 8))/(x^2 - 64)

Now, let's combine like terms in the numerator:

(4x + 32 + x + 2 - 3x + 24)/(x^2 - 64)

Combine the like terms further:

(2x + 58)/(x^2 - 64)

Since there are no common factors between the numerator and the denominator, the expression cannot be simplified any further.

Therefore, the simplified expression is:

(2x + 58)/(x^2 - 64)