Algebra Ch 11 Review

11.4 Simplify 1)15 – 5x 5x Do not cancel terms unless they are common factors of the numerator and denominator!!! = 5x is not a factor of all terms, therefore you cannot cancel 5x! 5(3 – x) 5(x) = 3 – x x A common mistake… 2) x 2 + 6x – x 2 (x + 3) 2 = DTS (3 – x)(3 + x) x – x =

5 7 x Multiplying and Dividing Rational Expressions x x

11.6 Adding/Subtracting Rational Expressions 1) 2222 x2x2x2x2 2) xxxx The LCD is 6x 3... The LCD is x(x + 1). (x + 1) =

11.7 Dividing Polynomials 9x² 3x 18 3x 12x 3x Divide 9x² + 12x – 18 by 3x 9x² + 12x – 18 3x = =3x x

11.7 Dividing Polynomials x² - 3x + 5 x + 2 Divide x²- 3x + 5 by x + 2 Ask: how many x’s in x²? x x Multiply x by x + 2 and subtract x² + 2x -5x + 5 Ask: how many x’s in -5x?-5 Multiply -5 by x + 2 and subtract -5x Remainder is 15 Quotient: Change signs when subtracting!

11.8 Solving by cross multiplying. 5 y + 2 y 3 =1) 5(3) = y(y + 2) 15 = y 2 + 2y = y 2 + 2y – 15 0 = (y + 5)(y – 3) y = -5, 3

3 x – 7 1 x 2 – 9x = -2) Clear the fraction by multiplying each term by the LCD!! Factor to help find the LCD!!! (x – 7)(x – 2) 3 x – = - (x – 7)(x – 2) The LCD is (x – 7)(x – 2)! 3x – 6+ x 2 – 9x + 14 = x 2 – 6x + 8 = -1 x 2 – 6x + 9 = 0 (x – 3) 2 = 0 x = Solving by clearing the fractions.

HW P # Look at your notes/Powerpoints to study -Make-ups today