सरल कीजिए (1)/(sqrt(3)-sqrt(2))

1.

$\frac{1}{5} \div \frac{3}{7} - \frac{4}{5} \times \frac{1}{2}$

Step 1: Division first (left to right).
$\frac{1}{5} \div \frac{3}{7} = \frac{1}{5} \times \frac{7}{3} = \frac{7}{15}$

Step 2: Multiplication.
$\frac{4}{5} \times \frac{1}{2} = \frac{4 \times 1}{5 \times 2} = \frac{4}{10} = \frac{2}{5}$

Step 3: Subtraction.
$\frac{7}{15} - \frac{2}{5} = \frac{7}{15} - \frac{6}{15} = \frac{1}{15}$

\dfrac{1{15}}

2.

$\frac{3}{5} - \frac{7}{8} \times \frac{5}{7}$

Step 1: Multiplication first (left to right).
$\frac{7}{8} \times \frac{5}{7} = \frac{7 \times 5}{8 \times 7} = \frac{5}{8}$

Step 2: Subtraction.
$\frac{3}{5} - \frac{5}{8}$
LCM of 5 and 8 is 40.
$\frac{3 \times 8}{5 \times 8} - \frac{5 \times 5}{8 \times 5} = \frac{24}{40} - \frac{25}{40} = -\frac{1}{40}$

-\dfrac{1{40}}

3.
$\frac{7}{5} - \frac{?}{10} = \frac{3}{5}$

Step 1: Isolate the unknown.
$\frac{?}{10} = \frac{7}{5} - \frac{3}{5} = \frac{4}{5}$

Step 2: Solve for ?.
$? = \frac{4}{5} \times 10 = 8$

8

4.
$(3 - ?) \times 2 = 10$

Step 1: Divide both sides by 2.
$3 - ? = \frac{10}{2} = 5$

Step 2: Solve for ?.
$? = 3 - 5 = -2$

-2

5.
$(5 + ?) \times 2 = 14$

Step 1: Divide both sides by 2.
$5 + ? = \frac{14}{2} = 7$

Step 2: Solve for ?.
$? = 7 - 5 = 2$

2

6.
$\begin{cases} x + y = 7 \\ x - y = 1 \end{cases}$

Step 1: Add the equations.
$(x + y) + (x - y) = 7 + 1$
$2x = 8$
$x = 4$

Step 2: Substitute x = 4 into first equation.
$4 + y = 7$
$y = 3$

x=4, y=3