Simplify Math Problems Solution1





In this page simplify math problems solution1 we are going to see solution of practice questions of the worksheet simplify math problems.

(1) Simplify the following rational expression into their lowest forms

(i)   (6 x² + 9 x)/(3 x² - 12 x)

Solution:

                        = (6 x² + 9 x)/(3 x² - 12 x)

We are going to bring 3x from the numerator and denominator

                   = [ 3 x (2 x + 3) ]/[ 3 x (x - 4) ]

                   = (2 x + 3)/(x - 4)


(ii)   (x² + 1)/(x⁴ - 1)

Solution:

                 = (x² + 1)/(x⁴ - 1)

                 = (x² + 1)/(x²)² - (1²)²

                 = (x² + 1)/[(x² + 1²)(x² - 1²)]

Now we are going to use the following algebraic formula to simplify this rational expression.

 a² - b² = (a + b ) (a -b)

                 = (x² + 1)/[(x² + 1²)(x + 1)(x - 1)]

                 = 1/(x + 1)(x - 1)

                 = 1/(x² - 1)


(iii)  (x³ - 1)/(x² + x + 1)

Solution:

                 = (x³ - 1)/(x² + x + 1)

Now we are going to use the following algebraic formula

 a³ - b³ = (a -b) (a² + ab + b²)

                 = (x - 1)(x² + x + 1)/(x² + x + 1)

                 = (x - 1)


(iv)  (x³ - 27)/(x² - 9)

Solution:

                     = (x³ - 27)/(x² - 9)

                 = (x³ - 3³)/(x² - 3²)

Now we are going to use the following algebraic formula

 a³ - b³ = (a -b) (a² + ab + b²)

 a² - b² = (a + b ) (a -b)

                 = [ (x - 3)(x² + 3x + 9) ]/[ (x + 3) (x -3) ]

                 = (x² + 3x + 9)/(x + 3)


(v)  (x⁴ + x² + 1)/(x² + x + 1)

Solution:

                     = (x⁴ + x² + 1)/(x² + x + 1)

Now we are going to use the following algebraic formula

(x⁴ + x² + 1) = (x² + 1)² - x²

                     = [ (x² + 1)² - x² ]/(x² + x + 1)

                     = [ (x² + 1 + x) (x² + 1 - x) ]/(x² + x + 1)

                     = [ (x² + x + 1 ) (x² - x + 1) ]/(x² + x + 1)

                 =  (x² - x + 1)

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