Question

expansion of (2x+3/x-1)^2...please don't fool i am spending my hardwork 21
points and want answer as urgent

Answer 1

Question :-

Expand -

$\sf \left( \dfrac{2x+3}{x-1}\right)^2$

Answer :-

$\implies\sf \left( \dfrac{2x+3}{x-1}\right)^2$

• $\sf \left( \dfrac{a}{b}\right)^n = \dfrac{a^n}{b^n}$

$\implies\sf \dfrac{(2x + 3)^2}{(x - 1)^2}$

• $\sf (a + b)^2 = a^2 + b^2 + 2ab$
• $\sf (a - b)^2 = a^2 + b^2 - 2ab$

$\implies\sf \dfrac{(2x)^2 + 3^2 + 2(2x)(3)}{(x)^2 + 1^2 - 2(x)(1)}$

$\implies\sf \dfrac{4x^2 + 9 + 12x}{x^2 + 1 - 2x}$

Additional information :-

$\boxed{\bigstar\:\:\textbf{\textsf{Algebric\:Identity}}\:\bigstar}\\\\1)\bf\:(A+B)^{2} = A^{2} + 2AB + B^{2}\\\\2)\sf\: (A-B)^{2} = A^{2} - 2AB + B^{2}\\\\3)\bf\: A^{2} - B^{2} = (A+B)(A-B)\\\\4)\sf\: (A+B)^{2} = (A-B)^{2} + 4AB\\\\5)\bf\: (A-B)^{2} = (A+B)^{2} - 4AB\\\\6)\sf\: (A+B)^{3} = A^{3} + 3AB(A+B) + B^{3}\\\\7)\bf\:(A-B)^{3} = A^{3} - 3AB(A-B) + B^{3}\\\\8)\sf\: A^{3} + B^{3} = (A+B)(A^{2} - AB + B^{2})$

$\bf{\dag}\:\:\underline{\text{Law of Exponents :}}\\\\ \bigstar\:\:\sf\dfrac{a^m}{a^n} = a^{m - n}\\\\ \bigstar\:\:\sf{(a^m)^n = a^{mn}}\\\\ \bigstar\:\:\sf(a^m)(a^n) = a^{m + n}\\\\ \bigstar\:\:\sf\dfrac{1}{a^n} = a^{-n}\\\\ \bigstar\:\:\sf\sqrt[\sf n]{\sf a} = (a)^{\dfrac{1}{n}}$