Please help with the following Thank you Operations on Ratio

Please help with the following. Thank you:)!

Operations on Rational Expressions Add and Subtract. 9/x - 9x/9 - 8x + 2 Complex Fractions Simplify. 9/b - 16/b + 7/7/b + 7/b + 7 Complex Fractions Simplify. x - 36/x/1 + 6/x

Solution

4. 9/x - 9x/ (9-8x) + 2

= 9/x - (9x + 18 -16x)/(9-8x)

= 9/x - (18 -7x)/(9-8x)

= (81 - 72x - 18x + 7x²)/ x(9-8x)

= (7x² - 90x + 81)/ x(9-8x)

5. [9/b -16/b+7] / [7/b + 7/b+7]

= [9b + 63 - 16b] / b(b+7) / [7b + 49 + 7b] / b(b+7)

= [63 - 7b] / [49 + 14b]

= 7(9 - b) / 7(7 + 2b)

= (9 - b) / (7 + 2b)

6. (x - 36/x) / (1 + 6/x)

= (x² - 36)/x / (x + 6)/x

= (x² - 36) / (x + 6)

= (x + 6)(x - 6) / (x + 6)

= x - 6