Simplify the expressions below.

1. $\large\frac{x^2-8x+16}{3x^2-10x-8}$ for $x\ne−\frac{2}{3}$ or $4$

   Step (a):

   Factor the numerator and denominator.

   $\frac{\left(x-4\right)\left(x-4\right)}{\left(3x+2\right)\left(x-4\right)}$

   Hint (a):

   After factoring, look for a Giant One to remove.

   Answer (a):

   $\frac{x-4}{3x+2}$

2. $\large\frac { 10 x + 25 } { 2 x ^ { 2 } - x - 15 }$ for $x ≠ −\frac { 5 } { 2 }$ or $3$

   Hint (b):

   Refer to part (a).

3. $\large \frac { ( k - 4 ) ( 2 k + 1 ) } { 5 ( 2 k + 1 ) } \div \frac { ( k - 3 ) ( k - 4 ) } { 10 ( k - 3 ) }$ for $k ≠ 3, 4 \text{ or } −\frac { 1 } { 2 }$

   Hint (c):

   This is division with fractions. Here is a sample division problem with numbers.

   $\frac{6}{5}\div\frac{24}{5}$

   Step 1: Rewrite as multiplication by taking the reciprocal of the divisor.

   $\frac{6}{5}\cdot\frac{5}{24}$

   Step 2: Factor $24$ and use the Commutative Property to rewrite the problem so
   there are Giant Ones.

   $\frac{5}{5}\cdot\frac{6\cdot1}{6\cdot4}$

   Step 3: Remove the Giant Ones.

   $\frac{1}{4}$

   Apply these steps to part (c).