Simplify equation

Question

( x/9 - 5/x²) ⁄ (x/3 + 3/x + 6/x²) 

Answer 1

(x/9 - 5/x²) ⁄ (x/3 + 3/x + 6/x²) 

 

Look at your numerator:

Lowest common denominator is 9x²

x/9 - 5/x² = x³/9x² - 45/9x² = (x³-45)/9x²

 

Look at the denominator:

Lowest common denominator is 3x²

(x/3 + 3/x + 6/x²) = x³/3x² + 9x/3x² + 18/3x² = (x³+9x+18)/(3x²)

 

(x/9 -5/x²)/(x/3+3/x+6/x²) = [(x³-45)/(9x²)]/[(x³+9x+18)/(3x²)]

 

= [(x³-45)/(9x²)][(3x²)/(x³+9x+18)]

 

= (x³-45)/[3(x³+9x+18)]

 

= (x³-45)/(3x³+27x+54)