ভাগ কর : (১ম রাশিকে ২য় রাশি দ্বারা)

$$\begin{gathered} \frac{3x^2}{2a}÷\frac{4y^2}{15zx} \\ =\frac{3x^2}{2a}\times \frac{15zx}{4y^2} \\ =\frac{45z{x}^3}{8a{y}^2} \end{gathered}$$

$$\begin{gathered} \frac{9a^2{b}^2}{4c^2}÷\frac{16a^3}{3c^3} \\ =\frac{9a^2{b}^2}{4c^2}\times \frac{3c^3}{16a^3} \\ =\frac{27bc}{64a} \end{gathered}$$

$\frac{21a^4{b}^4{c}^4}{4x^3{y}^3{z}^3}÷\frac{7a^2{b}^2{c}^2}{12xyz}$

$$\begin{gathered} =\frac{21a^4{b}^4{c}^4}{4x^3{y}^3{z}^3}\times \frac{12xyz}{7a^2{b}^2{c}^2} \\ =\frac{9a^2{b}^2{c}^2}{x^2{y}^2{z}^2} \end{gathered}$$

$\frac{x}{y}÷\frac{x+y}{y}$

$=\frac{x}{y}\times \frac{y}{x+y}$

$=\frac{x}{x+y}$

$\frac{{(a+b)}^2}{{(a-b)}^2}÷\frac{a^2-b^2}{a+b}$

$=\frac{{(a+b)}^2}{{(a-b)}^2}\times \frac{a+b}{a^2-b^2}$

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

$=\frac{{(a+b)}^2}{{(a-b)}^3}$

$\frac{x^3-y^3}{x+y}÷\frac{x^2+xy+y^2}{x^2+y^2}$

$=\frac{(x-y)(x^2+xy+y^2)}{x+y}\times \frac{x^2+y^2}{x^2+xy+y^2}$

$$\begin{gathered} =\frac{(x-y)(x^2+xy+y^2)(x+y)(x-y)}{(x+y)(x^2+xy+y^2)} \\ ={(x-y)}^2 \end{gathered}$$

$\frac{a^3+b^3}{a-b}÷\frac{a^2-ab+b^2}{a^2-b^2}$

$=\frac{a^3+b^3}{a-b}\times \frac{a^2-b^2}{a^2-ab+b^2}$

$$\begin{gathered} =\frac{(a+b)(a^2-ab+b^2) (a+b)(a-b)}{(a-b)(a^2-ab+b^2)} \\ ={(a+b)}^2 \end{gathered}$$

$\frac{x^2-7x+12}{x^2-4}÷\frac{x^2-16}{x^2-3x+2}$

$=\frac{x^2-3x-4x+12}{{\left(x\right)}^2-{\left(2\right)}^2}÷\frac{x^2-16}{x^2-x-2x+2}$

$=\frac{x(x-3)-4(x-3)}{(x+2)(x-2)}÷\frac{(x+4)(x-4)}{x(x-1)-2(x-1)}$

$=\frac{(x-3)(x-4)}{(x+2)(x-2)}\times \frac{(x-1) (x-2)}{(x+4)(x-4)}$

$=\frac{(x-1) (x-3)}{(x+2)(x+4)}$

$\frac{x^2-x-30}{x^2-36}÷\frac{x^2+13x+40}{x^2+x-56}$

=$\frac{x^2-6x+5x-30}{{\left(x\right)}^2-{\left(6\right)}^2}÷\frac{x^2+5x+8x+40}{x^2+8x-7x-56}$

$=\frac{x(x-6)+5(x-6)}{(x+6)(x-6)}÷\frac{x(x+5)+8(x+5)}{x(x+8)-7(x+8)}$

$=\frac{(x-6)(x+5)}{(x+6)(x-6)}÷\frac{(x+5)(x+8)}{(x+8)(x-7)}$

$=\frac{(x-6)(x+5)}{(x+6)(x-6)}\times \frac{(x+8)(x-7)}{(x+5)(x+8)}$

$=\frac{(x-7)}{(x+6)}$