Question

a) 1/х-2 - 1/х+2
б) 3а/1 × 5b/3a²
в) 3xy²/4a ÷ 13y/24a²b

Answer 1

$a)\frac{ 1 }{ x-2 } - \frac{ 1 }{ x+2 } = \frac{x+2}{\left(x-2\right)\left(x+2\right)}-\frac{x-2}{\left(x-2\right)\left(x+2\right)} = \frac{x+2-\left(x-2\right)}{\left(x-2\right)\left(x+2\right)} = \frac{x+2-x+2}{\left(x-2\right)\left(x+2\right)} = \frac{4}{\left(x-2\right)\left(x+2\right)} = \frac{4}{x^{2}-4} \\ b)\frac{ 3a }{ 1 } \times \frac{ 5b }{ 3a ^ { 2 } } = \frac{1}{1} \times \frac{5b}{a} = \frac{5b}{a} \\ c)\frac{ 3xy ^ { 2 } }{ 4a } \div \frac{ 13y }{ 24a ^ { 2 } b } = \frac{3xy^{2}\times 24a^{2}b}{4a\times 13y} = \frac{3\times 6abxy}{13} = \frac{18abxy}{13}$