Question

A²+8a+16)/15a²+3a * 25a²-1/16-a² при а=5​

Answer 1

Ответ:

Смотри решение на фото

Answer 2

To evaluate the expression $\frac{{a^2 + 8a + 16}}{{15a^2 + 3a}} \cdot \frac{{25a^2 - 1}}{{16 - a^2}}$ when $a = 5$, you can simply substitute $a$ with 5 and perform the calculations step by step.

First, substitute $a$ with 5 in each part of the expression:

$\frac{{5^2 + 8 \cdot 5 + 16}}{{15 \cdot 5^2 + 3 \cdot 5}} \cdot \frac{{25 \cdot 5^2 - 1}}{{16 - 5^2}}$

Now, calculate the values in the numerators and denominators:

Numerator of the first fraction: $5^2 + 8 \cdot 5 + 16 = 25 + 40 + 16 = 81$

Denominator of the first fraction: $15 \cdot 5^2 + 3 \cdot 5 = 15 \cdot 25 + 15 = 375$

Numerator of the second fraction: $25 \cdot 5^2 - 1 = 125 \cdot 25 - 1 = 3124$

Denominator of the second fraction: $16 - 5^2 = 16 - 25 = -9$

Now, substitute these values back into the expression:

$\frac{{81}}{{375}} \cdot \frac{{3124}}{{-9}}$

Now, calculate each fraction separately:

$\frac{{81}}{{375}}$ simplifies to $\frac{{9}}{{45}}$, and both the numerator and denominator can be divided by 9:

$\frac{{9}}{{45}} = \frac{{1}}{{5}}$

Now, calculate the second fraction:

$\frac{{3124}}{{-9}} = -\frac{{3124}}{{9}}$

So, the final result is:

$\frac{{1}}{{5}} \cdot (-\frac{{3124}}{{9}})$

To multiply fractions, multiply the numerators together and the denominators together:

$\frac{{1 \cdot (-3124)}}{{5 \cdot 9}} = \frac{{-3124}}{{45}}$

So, when $a = 5$, the expression $\frac{{a^2 + 8a + 16}}{{15a^2 + 3a}} \cdot \frac{{25a^2 - 1}}{{16 - a^2}}$ simplifies to $-\frac{{3124}}{{45}}$.