Question

X+3/x+2=3x-7/2x-3 find the value of x

Answer 1

$\bf Given: \tt \dfrac{x\ +\ 3}{x\ +\ 2}\ =\ \dfrac{3x\ -\ 7}{2x\ -\ 3}\\\\\\\bf To\ find:\ \tt The\ value\ of\ x.\\\\\\\bf Answer:\\\\\\\tt \dfrac{x\ +\ 3}{x\ +\ 2}\ =\ \dfrac{3x\ -\ 7}{2x\ -\ 3}\\\\\\\bf Cross\ multiplying,\\\\\\\tt (x\ +\ 3)(2x\ -\ 3)\ =\ (3x\ -\ 7)(x\ +\ 2)\\\\\\2x^2\ -\ 3x\ +\ 6x\ -\ 9\ =\ 3x^2\ +\ 6x\ -\ 7x\ -\ 14\\\\\\2x^2\ +\ 3x\ -\ 9\ =\ 3x^2\ -\ x\ -\ 14\\\\\\2x^2\ -\ 3x^2\ +\ 3x\ +\ x\ =\ 9\ -\ 14\\\\\\-x^2\ +\ 4x\ =\ -5\\\\\\x^2\ -\ 4x\ =\ 5$

$\tt x^2\ -\ 4x\ -\ 5$

By splitting the middle term,

$\tt x^2\ +\ 1x\ -5x\ -\ 5\\\\\\x(x\ +\ 1)\ -\ 5(x\ +\ 1)\\\\\\(x\ -\ 5)(x\ +\ 1)\\\\\\\bf x\ =\ 5\ \tt or\ \bf x\ =\ -1$