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# simplify the rational expression

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

### 2 Answers by Expert Tutors

Steve S. | Tutoring in Precalculus, Trig, and Differential CalculusTutoring in Precalculus, Trig, and Diffe...
5.0 5.0 (3 lesson ratings) (3)
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f(x) = (1/(x+1)+1/(x+2)) / (1/(x+2)+1/(x+3))

x ≠ -1,-2,-3

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

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

f(x) = ((x+2)(x+3)+(x+1)(x+3))

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

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

f(x) = ((x+3)(2x+3)) / ((x+1)(2x+5)), x ≠ -1,-2,-5/2,-3

f(x) = (2x^2+3x+6x+9) / (2x^2+5x+2x+5), x ≠ -1,-2,-5/2,-3

f(x) = (2x^2+9x+9) / (2x^2+7x+5), x ≠ -1,-2,-5/2,-3

Horizontal asymptote at y = 1,
Vertical asymptotes at x = -1 and x = -5/2,
Zeros at x = -3 and x = -3/2, except
Holes at x = -2 and x = -3, (so no zero at x = -3),
y-intercept at y = ((3)(3)) / ((1)(5)) = 9/5.

See GeoGebra sketch at http://www.wyzant.com/resources/files/259912/hard_rational_function.

Parviz F. | Mathematics professor at Community CollegesMathematics professor at Community Colle...
4.8 4.8 (4 lesson ratings) (4)
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1/ (X+1 )  + 1/ ( X +2)   /   1/( X+2) + 1/ ( X +3) =

1 / ( X + 1 ) + 1 / ( X +2 ) =  (2X +3) / (X + 1 ) ( X + 2)

1/ ( X +2 ) + 1/ ( X +3 )   =  ( 2X +5 ) / ( X +2 ) ( X+3)

( 2X +3 )  / ( X+ 1) ( X +2 )  / ( 2X +5 ) /( X + 2 ) ( X+3)

( 2X + 3) / ( X +1 ) ( X +2 )  /  ( 2X +5 ) / ( X +2 ) ( X +3 )

( 2X + 3 ) / ( X+1 ) ( X +2 )* ( ( X+2) ( X +3) / ( 2X + 5)

(2 X + 3 ) * ( X+3) / ( X +1 ) * ( 2X + 5)

(2X^2  + 9x + 9 ) / ( 2X^2 + 7X + 5 )