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10-53.

Which of the expressions below are equal to $1$ ? (Note: More than one answer is possible!)

Hint:

Any fraction where the numerator and denominator are the same is equal to $1$ .

$\frac { 2 x + 3 } { 3 + 2 x }$
Hint (a):
Rearrange to see if the numerator and denominator are equal.
$\frac{2x+3}{2x+3}$
Answer (a):
The fraction is equal to $1$ .

$\frac{6x-12}{6\left(x-2\right)}$
Hint (b):
Simplify the expression.
$\frac{6x-12}{6x-12}$
Answer (b):
The fraction is equal to $1$ .

$\frac{\left(2x-3\right)\left(x+2\right)}{2x^2+x-6}$
Hint (c):
Factor the denominator using a generic rectangle and the diamond pattern found in earlier chapters.

$\frac { x } { 2 } \div \frac { 2 } { x }$
Hint (d):
Change the expression to a product.
$\left(\frac{x}{2}\right) \left(\frac{x}{2}\right)$
Does this product equal $1$ ?

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