Question

Looking for some help on some subtraction of rational fractions :)

Which expression is equivalent to X^2 - 5 / x^2 + 5x - 14 = x + 3 / x + 7?

If at all possible, any help/explanation of the process would be greatly appreciated ^u^

Answer 1

Hello! I'd be happy to help you with your math question. To find the equivalent expression, we first need to simplify both sides of the equation. We can start by factoring the quadratic in the denominator of the left side:

X^2 - 5 / (x - 2)(x + 7) = (x + 3) / (x + 7)

Next, we can cross-multiply to get rid of the fractions:

(x + 3)(x - 2)(x + 7) = (x + 7)(X^2 - 5)

Expanding both sides and simplifying, we get:

x^3 + 8x^2 - 11x - 42 = x^3 + 7x^2 - 5x - 35

Simplifying further, we get:

x^2 - 6x - 7 = 0

We can now factor this quadratic to get:

(x - 7)(x + 1) = 0

Therefore, the equivalent expression is:

x^2 - 5 / x^2 + 5x - 14 = x + 3 / x + 7 if and only if x equals -1 or 7. I hope this helps! Let me know if you have any further questions.

Answer 2

I hope this helped you!

Answer 3

Wow! That was quick, thank you!! This helps a ton, thank you again :)