Rational expressions

Question

Simplify the rational Expressions by multiplying or dividing. List any undefin values.

 

1. X²-12x+32/x²-6x-16 • x+2/x²-16 

 

2. X-7/x²-2x-35 ÷ 9x+54/10x+50

 

3. X/x+1 + x+2/x²-1

 

4. X+2/x-6 - x²+5x+14/x²-2x-24

Answer 1

For problems 1 and 2, factor first, then cancel common factors.

 

1. (x²-12x+32)/(x²-6x-16) • (x+2)/(x²-16)

 

    = (x-8)(x-4)/[(x-8)(x+2)]•(x+2)/[(x-4)(x+4)] 

 

    = 1/(x+4)

 

Problem 2 is done in a similar manner.

 

For problems 3 and 4, find the LCD, then add or subtract.

 

4. (x+2)/(x-6) - (x²+5x+14)/(x²-2x-24)

 

   = (x+2)/(x-6) - (x²+5x+14)/[(x-6)(x+4)]

 

   = (x+2)(x-6)/[(x-6)(x+4)] - (x²+5x+14)/[(x-6)(x+4)]

 

   = (x²-4x-12)/[(x-6)(x+4)] - (x²+5x+14)/[(x-6)(x+4)]

 

   = (-9x-26)/[(x-6)(x+4)]

 

Do problem 3 in a similar way.