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))
