# Write the rational expression in simplest form. 25.x^3+5x^2+6x over x^2-4 26.x^2+8x-20 over x^2+11x+10 27.y^2-7y+12 over y^2+3y-18?

• Write the rational expression in simplest form. 25.x^3+5x^2+6x over x^2-4 26.x^2+8x-20 over x^2+11x+10 27.y^2-7y+12 over y^2+3y-18?

Answer #1 | 01/09 2014 02:46
x³ + 5x² ³ + 6x --------------------- .... x² - 4 1) Factor out an x from each term in the numerator After you have factored, you will have this: x ( x² + 5x + 6x ) --------------------- .... x² - 4 2) Factor the numerator and factor the denominator as the Difference of Two Squares, like this: x ( x + 2 )( x + 3 ) --------------------- ( x + 2 )( x - 2 ) 3) Cancel ( x + 2 ) from the top and from the bottom, so that you end up with this: x ( x + 3 ) -------------- <-- answer ( x - 2 ) ~ ~ ~ ~ ~ ~ ~ x² + 8x - 20 ------------------ x² +11x + 10 1) Factor the numerator and the denominator, like this: ( x + 10 )( x - 2 ) ----------------------- ( x + 10 )( x + 1 ) 2) Cancel ( x + 10 ) from the top and from the bottom, so that you end up with this: ( x - 2 ) ----------- <-- Answer ( x + 1 ) ~ ~ ~ ~ ~ ~ ~ ~ y² - 7y + 12 ----------------- y² +3y - 18 1) Factor the top and the bottom to see if there are any common factors that you could cancel After you have factored, you have this: ( y - 3 )( y - 4 ) -------------------- ( y - 3 )( y + 6 ) 2) Cancel ( y - 3 ) from the top and the bottom, so that you end up with this: ( y - 4 ) ----------- <-- Answer ( y + 6 )
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Answer #41 | 01/09 2014 02:19
(x^3 +5x^2 +6x)/(x^2 -4) = (x)(x^2 +5x +6)/((x-2)(x+2)) = (x)(x+3)(x+2)/((x-2)(x+2)) = (x)(x+3)/(x-2) (x^2 +8x -20)/(x^2 +11x +10) = (x+10)(x-2)/((x+10)(x+1)) = (x-2)/(x+1) (y^2 -7y +12)/(y^2 +3y -18) = (y-3)(y-4)/((y+6)(y-3)) = (y-4)/(y+6)
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