Question

find the root of following quadratic equations x+3/x+2=3x-7/2x-3​

Answer 1

$\huge{\underline{\underline{\boxed{\sf{\purple{Answer}}}}}}$

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

ʙʏ ᴄʀᴏss ᴍᴜʟᴛɪᴘʟʏɪɴɢ

$(x + 3)(2x - 3) = (x + 2)(3x - 7) \\2 x {}^{2} - 3x + 6x - 9 = 3 {x}^{2} - 7x + 6x - 14 \\ 2x {}^{2} - 3x {}^{2} + 3x - 9 = - x - 14 \\ - x {}^{2} + 3x + x - 9 + 14 = 0 \\ - x {}^{2} + 4x + 5 = 0 \\ x {}^{2} - 4x - 5 = 0$

ʙʏ ᴜsɪɴɢ ᴍɪᴅᴅʟᴇ ᴛᴇʀᴍ sᴘʟɪᴛᴛɪɴɢ ᴍᴇᴛʜᴏᴅ :-

$x {}^{2} - 4x - 5 = 0 \\ x {}^{2} - 5x + x - 5 = 0 \\ x(x - 5) + 1(x - 5) = 0 \\ (x - 5)(x + 1) = 0 \\ x = 5 ,- 1$

5 ᴀɴᴅ -1 ᴀʀᴇ ᴛʜᴇ ʀᴏᴏᴛs ᴏғ ᴛʜᴇ ɢɪᴠᴇɴ ǫᴜᴀᴅʀᴀᴛɪᴄ ᴇǫᴜᴀᴛɪᴏɴ