Question

solve the quadratic equation​

Answer 1

x+1(2x-5)=x-1(3x-7)

2x^2-5x+2x-5=3x^2-3x-7x+7

-3x=1x^2-10x+7+5

x^2-7x+12=0

by applying quadratic formula you get

x=4 or 3

Answer 2

$\huge \boxed{ \red{ \mathfrak{solution}}}$

To solve :

$\bold{\frac{x + 1}{x - 1} = \frac{3x - 7}{2x - 5} }$

By cross multiplication :

$\implies (x + 1)(2x - 5) = (3x - 7)(x - 1) \\ \\ \implies 2 {x}^{2} - 5x + 2x - 5 = 3 {x}^{2} - 3x - 7x + 7 \\ \\ \implies2 {x}^{2} - 3x - 5 = 3 {x}^{2} - 10x + 7 \\ \\ \implies \: 3 {x}^{2} - 2 {x}^{2} - 10x + 3x + 7 + 5 = 0 \\ \\ \implies \: {x}^{2} - 7x + 12 = 0$

Now split the middle term :

$\star \: {x}^{2} - 7x + 12 = 0 \\ \\ \star \: {x}^{2} - 4x - 3x + 12 = 0\\ \\ \star \: x(x - 4) - 3(x - 4) = 0 \\ \\ \star \: (x - 3)(x - 4) = 0$

$\star \: x - 3 = 0 \\ \\ \rightarrow \: x =3$

And

$\star \: x - 4 = 0 \\ \\ \rightarrow \:x = 4$

Hence ,the value of X is

$\huge \: \boxed{ \green{3 \: \: \mathfrak{ And} \: \: 4}}$