Simplify Math Problems Solution2





In this page simplify math problems solution2 we are going to see solution of practice questions of the worksheet simplify math problems.

(vi)  (x³ + 8)/(x⁴ + 4 x² + 16)

Solution:

                        = (x³ + 8)/(x⁴ + 4 x² + 16)

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

(x⁴ + x² + 1) = (x² + 1)² - x²

(x⁴ + 4 x² + 16) = (x² + 4)² - (2 x)²

                        = (x³ + 2³)/[(x² + 4) + (2 x)][(x² + 4) - (2 x)]

                        = (x + 2)(x² + 2 x + 4)/[(x² + 2 x + 4)][(x² - 2 x + 4)]

                   = (x + 2)/(x² - 2 x + 4)


(vii) (2 x² + x - 3)/(2 x² + 5 x + 3)  

Solution:

                        = (2 x² + x - 3)/(2 x² + 5 x + 3)  

Now we are going to factorize the above quadratic equations

                        = (x  - 1) (2x + 3)/(x + 1)(2x + 3)

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


(viii) (2 x⁴ - 162)/(x² + 9) (2 x - 6)

Solution:

                        = (2 x⁴ - 162)/(x² + 9) (2 x - 6)

                        = 2 (x⁴ - 81)/(x² + 9) 2 (x - 3)

                        = (x⁴ - 3⁴)/(x² + 9) (x - 3)

                        = [ (x²)² - (3²)² ]/(x² + 9) (x - 3)

                        = [ ((x²) + (3²)) ((x²) - (3²))]/(x² + 9) (x - 3)

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

                        =  (x + 3) 


(ix)   [(x - 3) (x² - 5 x + 4)]/[ (x - 4) (x² - 2 x - 3) ]

Solution:

                        = [(x - 3) (x² - 5 x + 4)]/[(x - 4) (x² - 2 x - 3)]

Now we are going to factorize the above quadratic equations

                        = [(x - 3) (x - 1) (x - 4)]/[(x - 4) (x - 3) (x + 1)]

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

simplify math problems solution2  simplify math problems solution2