Question

СРОЧНО СРОЧНО СРОЧНО​

Answer 1

1.

$\frac{6a}{a + 3} + \frac{7}{a - 3} - 6 = \frac{6a}{a + 3} + \frac{7}{a - 3} - \frac{6}{1} = \frac{6a \times (a - 3)}{(a + 3) \times (a - 3)} + \frac{7 \times (a + 3)}{(a - 3) \times (a + 3)} - \frac{6 \times (a + 3)(a - 3)}{(a + 3)(a - 3)} = \frac{6a(a - 3) + 7(a + 3) - 6(a + 3)(a - 3)}{(a + 3)(a - 3)} = \frac{6 {a}^{2} - 18a + 7a + 21 - 6( {a}^{2} - {3}^{2} ) }{ {a}^{2} - {3}^{2} } = \frac{6 {a}^{2} - 18a + 7a + 21 - 6 {a}^{2} + 54 }{ {a}^{2} - 9} = \frac{ - 11a + 75}{ {a}^{2} - 9}$

2.

$\frac{2a}{a - 5} - \frac{ {a}^{2} + 4a}{8} \times \frac{14}{a + 4} = \frac{2a}{a - 5} - \frac{ ({a}^{2} + 4a) \times 14}{8 \times (a + 4)} = \frac{2a}{a - 5} - \frac{a(a + 4) \times 2 \times 7}{2 \times 4 \times (a + 4)} = \frac{2a}{a - 5} - \frac{7a}{4} = \frac{2a \times 4}{(a - 5) \times 4} - \frac{7a \times (a - 5)}{4 \times (a - 5)} = \frac{2a \times 4 - 7a \times (a - 5)}{4(a - 5)} = \frac{8a - 7 {a}^{2} + 35a}{4a - 20} = \frac{ - 7 {a}^{2} + 43a}{4a - 20}$

3.

$( \frac{b}{b - 7} - \frac{b}{b + 7} ) \div \frac{7b}{b + 7} = ( \frac{b \times (b + 7)}{(b - 7) \times (b + 7)} - \frac{b \times (b - 7)}{(b + 7) \times (b - 7)} ) \div \frac{7b}{b + 7} = \frac{b \times (b + 7) - b \times (b - 7)}{(b - 7) \times (b + 7)} \div \frac{7b}{b + 7} = \frac{ {b}^{2} + 7b - {b}^{2} + 7b}{(b - 7)(b + 7)} \div \frac{7b}{b + 7} = \frac{14b}{(b - 7)(b + 7)} \div \frac{7b}{b + 7} = \frac{14b}{(b - 7)(b + 7)} \times \frac{b + 7}{7b} = \frac{14b \times (b + 7)}{(b - 7)(b + 7) \times 7b} = \frac{2}{b - 7}$