How do I simplify this expression?

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Answer 1 · 2018-02-21T05:36:16

#=>color(green)( (4x^2 - 1) / (x^2 + 7x + 12)#

#Nr = (2x^2 + 5x + 2) / (x^2 + 2x - 3)#

#=> = (2x^2 + 4x + x + 2) / (x^2 + 3x - x - 3)#

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

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

Similarly, let’s factorize the denominator

#Dr = (x^2 + 6x + 8) / (2x^2- 3x + 1)#

#=> (x^2 + 4x + 2x + 8) / (2x^2 - 2x - x + 1)#

#=> (x(x + 4) + 2(x + 4)) / ((2x (x - 1) -1 (x - 1))#

#=> ((x + 2) (x + 4)) / ((2x-1) (x - 1))#

#(Nr) / (Dr) = ((cancel(x+2)(2x+1)) / ((x+3) cancel(x-1))) / ( (cancel(x + 2) (x + 4)) / ((2x-1)cancel (x - 1)))#

#=> ((2x + 1) (2x - 1)) / ((x + 3) (x + 4))#

#=>color(green)( (4x^2 - 1) / (x^2 + 7x + 12)#