Question

Рациональные дроби 8 класс решите пж срочно! ДАЮ 100 БАЛЛОВ

Answer 1

1.

$\frac{4}{15a ^{2} {b}^{3} } + \frac{5}{12 {a}^{3}b } = \frac{4a \times 4}{4a \times 15 {a}^{2} {b}^{3} } + \frac{5 {b}^{2} \times 5 }{5 {b}^{2} \times 12 {a}^{3} b} = \frac{16a}{60 {a}^{3} {b}^{3} } + \frac{25 {b}^{2} }{60 {a}^{3} {b}^{3} } = \frac{16a + 25 {b}^{2} }{60 {a}^{3} {b}^{3} } </p><p>$

2.

$\frac{x}{ {x}^{2} - 49 } + \frac{7}{ {x}^{2} - 49} = \frac{x}{ {x}^{2} - 49} + \frac{7}{ - ( {x}^{2} - 49 )} = \frac{x}{ {x}^{2} - 49 } - \frac{7}{ {x}^{2} - 49} = \frac{x - 7}{ {x}^{2} - 49} = \frac{x - 7}{(x - 7)(x + 7)} = \frac{1}{x + 7}$

3.

$\frac{a}{2a + 2b} - \frac{3}{5a + 5b} = \frac{a}{2(a + b)} - \frac{3}{5(a + b)} = \frac{5a - 6}{10(a + b)} = \frac{5a - 6}{10a + 10b}$

4.

$\frac{7}{m - 6} - \frac{10m}{ {m}^{2} - 36} + \frac{5}{m + 6} = \frac{7}{m - 6} - \frac{10m}{(m - 6)(m + 6)} + \frac{5}{m + 6} = \frac{7(m + 6) - 10m + 5(m - 6)}{(m - 6)(m + 6)} = \frac{7m + 42 - 10m + 5m - 30}{(m - 6)(m + 6)} = \frac{2m + 12}{(m - 6)(m + 6)} = \frac{2(m + 6)}{(m - 6)(m + 6)} = \frac{2}{m - 6}$

5.

$\frac{3}{16 {a}^{3}b } - \frac{5}{12a {b}^{2} } = \frac{3b \times 3}{3b \times 16 {a}^{3} b} - \frac{4 {a}^{2} \times 5}{4 {a}^{2} \times 12a {b}^{2} } = \frac{9b}{48 {a}^{3} {b}^{2} } - \frac{20 {a}^{2} }{48 {a}^{3} {b}^{2} } = \frac{9b - 20 {a}^{2} }{48 {a}^{3} {b}^{2} } </p><p>$

6.

$\frac{ {a}^{2} }{a - 9} + \frac{81}{9 - a} = \frac{ {a}^{2} }{a - 9} + \frac{81}{ - (a - 9)} = \frac{ {a}^{2} }{a - 9} - \frac{81}{a - 9} = \frac{ {a}^{2} - 81 }{a - 9} = \frac{(a - 9)(a + 9)}{a - 9} = a + 9$

7.

$\frac{4}{7a - 7b} + \frac{a}{3a - 3b} = \frac{4}{7(a - b)} + \frac{a}{3(a - b)} = \frac{12 + 7a}{21(a - b)} = \frac{12 + 7a}{21a - 21b}$

8.

$\frac{10c}{ {c}^{2} - 16 } - \frac{5}{c + 4} + \frac{7}{c - 4} = \frac{10c}{(c - 4)(c +4) } - \frac{5}{c + 4} + \frac{7}{c - 4} = \frac{10c - 5(c - 4) + 7(c + 4)}{(c - 4)(c + 4)} = \frac{10c - 5c + 20 + 7c + 28}{(c - 4)(c + 4)} = \frac{12c + 48}{(c - 4)(c + 4)} = \frac{12(c + 4)}{(c - 4)(c + 4)} = \frac{12}{c - 4}$