# SOLUTION: Show each step in multiplying/dividing the following rational expressions: [(14x - 7)/(x^2 + 3x - 4)] · [(x^2 + 6x + 8)/(2x^2 + 5x - 3)] ÷ [(x^2 + 2x)/(x^2 + 2x - 3)]

Algebra ->  Algebra  -> Equations -> SOLUTION: Show each step in multiplying/dividing the following rational expressions: [(14x - 7)/(x^2 + 3x - 4)] · [(x^2 + 6x + 8)/(2x^2 + 5x - 3)] ÷ [(x^2 + 2x)/(x^2 + 2x - 3)]       Log On

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 Click here to see ALL problems on Equations Question 22394: Show each step in multiplying/dividing the following rational expressions: [(14x - 7)/(x^2 + 3x - 4)] · [(x^2 + 6x + 8)/(2x^2 + 5x - 3)] ÷ [(x^2 + 2x)/(x^2 + 2x - 3)] Answer by AnlytcPhil(1277)   (Show Source): You can put this solution on YOUR website!``` 14x - 7 x2 + 6x + 8 x2 + 2x ----------- · ------------- ÷ ----------- x2 + 3x - 4 2x2 + 5x - 3 x2 + 2x - 3 Invert the divided fraction and change the division to multiplication: 14x - 7 x2 + 6x + 8 x2 + 2x - 3 ----------- · ------------- · ----------- x2 + 3x - 4 2x2 + 5x - 3 x2 + 2x Factor all numerators and denominators: 7(2x - 1) (x + 4)(x + 2) (x + 3)(x - 1) ------------- · --------------- · -------------- (x + 4)(x - 1) (x + 3)(2x - 1) x(x + 2) Write the product of the numerators over the product of the denominators: 7(2x - 1)(x + 4)(x + 2)(x + 3)(x - 1) ------------------------------------- (x + 4)(x - 1)(x + 3)(2x - 1)x(x + 2) Cancel the (2x - 1)'s 7(2x - 1)(x + 4)(x + 2)(x + 3)(x - 1) ------------------------------------- (x + 4)(x - 1)(x + 3)(2x - 1)x(x + 2) 7(x + 4)(x + 2)(x + 3)(x - 1) ----------------------------- (x + 4)(x - 1)(x + 3)x(x + 2) Cancel the (x + 4)'s 7(x + 4)(x + 2)(x + 3)(x - 1) ----------------------------- (x + 4)(x - 1)(x + 3)x(x + 2) 7(x + 2)(x + 3)(x - 1) ---------------------- (x - 1)(x + 3)x(x + 2) Cancel the (x + 2)'s 7(x + 2)(x + 3)(x - 1) ---------------------- (x - 1)(x + 3)x(x + 2) 7(x + 3)(x - 1) --------------- (x - 1)(x + 3)x Cancel the (x - 1)'s 7(x + 3)(x - 1) --------------- (x - 1)(x + 3)x 7(x + 3) -------- (x + 3)x Cancel the (x + 3)'s 7(x + 3) -------- (x + 3)x 7 --- x Edwin AnlytcPhil@aol.com```