Question

I need help with this math question (complex fractions and rational expressions). For the answer, I need a step-by-step explanation so I can understand it, thank you :) I tried putting it into Symbolab to understand it but that wasn't very helpful so I think human assistance would be more beneficial haha. - $(\frac{(7x^{2} + 5x) }{x^{2} + 1 } ) - (\frac{5x}{x^{2} -6})$

Answer 1

Step-by-step explanation:

-(7x² + 5x) / (x² + 1) − 5x / (x² − 6)

To add or subtract fractions, you need a common denominator.

The common denominator of these fractions is (x² + 1) (x² − 6).

Multiply the first fraction by (x² − 6) / (x² − 6).

-(7x² + 5x) (x² − 6) / ((x² + 1) (x² − 6))

-(7x⁴ + 5x³ − 42x² − 30x) / ((x² + 1) (x² − 6))

(-7x⁴ − 5x³ + 42x² + 30x) / ((x² + 1) (x² − 6))

Multiply the second fraction by (x² + 1) / (x² + 1).

5x (x² + 1) / ((x² − 6) (x² + 1))

(5x³ + 5x) / ((x² − 6) (x² + 1))

Subtract the fractions.

(-7x⁴ − 5x³ + 42x² + 30x − 5x³ − 5x) / ((x² + 1) (x² − 6))

(-7x⁴ − 10x³ + 42x² + 25x) / ((x² + 1) (x² − 6))