Question

4а+7/а^2-4 - 3а+5/а^2-4

Answer 1

(4a+7-3a-5)/a^2-4=a+2/(a+2)(a-2)=1/а-2
a+2 и а+2 сокращается

Answer 2

To simplify the given expression, we need to combine the fractions and perform some algebraic manipulations. The expression is:

$\frac{4a + \frac{7}{a^2 - 4} - (3a + \frac{5}{a^2 - 4})}{1}$

Step 1: Combine the fractions in the numerator.

$\frac{4a + \frac{7 - 5}{a^2 - 4}}{1}$

Step 2: Simplify the numerator further.

$\frac{4a + \frac{2}{a^2 - 4}}{1}$

Step 3: Find a common denominator for the terms in the numerator.

The common denominator for the expression is $(a^2 - 4)$. So, we need to express $\frac{4a}{1}$ and $\frac{2}{a^2 - 4}$ with this common denominator.

$\frac{4a(a^2 - 4)}{(a^2 - 4)} + \frac{2}{a^2 - 4}$

Step 4: Combine the terms in the numerator.

$\frac{4a(a^2 - 4) + 2}{a^2 - 4}$

Step 5: Expand the numerator.

$\frac{4a^3 - 16a + 2}{a^2 - 4}$

The simplified expression is:

$\frac{4a^3 - 16a + 2}{a^2 - 4}$