Simplifying Algebraic Expressions with Indices or Factoring

Questions that ask the student to simplify a rational algebraic expression by factoring and cancelling terms involving powers of variables.

turkey-yks 2011 Q8 View
$$\frac { a ^ { 4 } - a ^ { 3 } } { a ^ { 4 } + a ^ { 2 } } \cdot \frac { a ^ { 2 } + 1 } { a ^ { 2 } - a }$$
Which of the following is the simplified form of this expression?
A) $a - 1$
B) a
C) 1
D) $a + 1$
E) $a ^ { 2 } + 1$
turkey-yks 2012 Q5 View
$$\frac { x ( y + z ) + z ( y - x ) } { x ^ { 2 } + x y + x z + y z }$$
Which of the following is the simplified form of this expression?
A) $\frac { x } { x + y }$
B) $\frac { y } { x + y }$
C) $\frac { z } { x + z }$
D) $\frac { y } { x + z }$
E) $\frac { y } { y + z }$