Perform indicated operation and simplify Perform indicated o

Perform indicated operation and simplify

Perform indicated operation and simplify x^3-12x+27/x-3/5x^2-45x/x+7

Solution

We have x² - 12x + 27 = x²- 9x - 3x + 27 = x ( x - 9) - 3 ( x - 9) = (x - 3) (x - 9). Therefore ( x² -12x + 27) / (x - 3) =

(x - 3) (x - 9) / ( x - 3) = (x -9) Also, 5x² - 45x = 5x ( x - 9) Therefore, [(x² - 12x + 27) /( x -3)] / [(5x² - 45x)/ (x + 7)] =

(x - 9) / [ 5x ( x - 9) / (x + 7) = (x - 9) / (x -9) *(x + 7)/ 5x =( x + 7) / 5x