Question

Simplify the following expression:

$\frac{\frac{5}{9} \times \frac{5}{9} - \frac{4}{9} \times \frac{4}{9}}{\frac{5}{9} - \frac{4}{9}}$

• A. 1
• B. 0
• C. 9
• D. 1/9

Answer 1

Answer:

A. 1

The value of the given expression is 1.

Using Algebraic Identity (Fastest)

Notice that the expression follows the form of the difference of squares identity: $\frac{a^2 - b^2}{a - b}$

Let $a = \frac{5}{9}$ and $b = \frac{4}{9}$. The expression becomes:
$\frac{a \times a - b \times b}{a - b} = \frac{a^2 - b^2}{a - b}$

Since $a^2 - b^2 = (a - b)(a + b)$, we can substitute and simplify:
$\frac{(a - b)(a + b)}{a - b} = a + b$

Now substitute the values of $a$ and $b$ back into the simplified expression:
$\frac{5}{9} + \frac{4}{9} = \frac{5 + 4}{9} = \frac{9}{9} = \mathbf{1}$