ALGEBRA 2Exam 5 coltll Describe and correct the error 12 15

ALGEBRA 2-Exam 5 - coltll Describe and correct the error. 12. 15x -9x-6,6x-6x-12 - -3 3 (Sx+3x+13x-3x+3) 15x-15x +15x 9x-9x2+9x 3x2-3x+3 -15x-6x +9x2 +6x+3 2x + 4 2x14 x 13, 2x+4 . r + 2x +4 x+2 x-2 (x-2 2x2 +8x+8 x-4x+4 x +4x +12 x-4 +2 2. 2 36

Solution

12) the error is in step 2

since we cannot cancel out the numerator by denominator in this way as there is minus sign between the terms

( 15x^2 - 9x - 6) / ( 3x^2 -3x - 6) * ( 6x^2 - 6x -12 ) / ( 2x^2 + 2x - 4)

factoring each expression

3(5x+2)(x-1) / 3(x+1)(x-2) * 6(x+1)(x-2) / 2(x+2)(x-1)

on simplifying we get

3 (5x+2) / (x+2)

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

error is we cannot cancel out x-2 from top and bottom since there is minus sign in between

on simplifying we get

{2(x+2)^2 - (x-2)^2 } / (x-2)(x+2)

( x^2 + 12 x + 4 ) / (x-2)(x+2)