Question

12x+17/3x+1 - 2x+15/X+7=16/5​

Answer 1

Question

$\sf{Solve= \dfrac{12x+17}{3x+1} -\dfrac{ 2x+15}{X+7}=3\dfrac{1}{5}}$

$\sf{Answer \bold{ = -68/9\ \ \ \ or\ \ 3}}$

Step by step explanation:

$\sf{\Rightarrow\dfrac{12x+17}{3x+1} -\dfrac{ 2x+15}{X+7}=\dfrac{16}{5}}$

$\sf{\Rightarrow\dfrac{12x+17}{3x+1} -\dfrac{ 2x+15}{x+7}=\dfrac{16}{5}}$

$\sf{\Rightarrow \dfrac{12x+17}{3x+1} -\dfrac{ 2x+15}{X+7}=\dfrac{16}{5}}$

$\sf{\Rightarrow \frac{((12x+17)(x+7) - (2x+15)(3x+1))}{((x+7)(3x+1))} = \frac{16}{ 5}}$

$\sf{\Rightarrow \frac{(12 {x}^{2} +101x+119-6 {x}^{2} -47x-15)}{(3 {x}^{2} +22x+7)} = \frac{16}{ 5}}$

$\sf{\Rightarrow\frac{(6{x}^{2} +54x+104 )}{(3 {x}^{2} +22x+7)} = \frac{16}{ 5} }$

$\sf{\Rightarrow {5(6 {x}^{2} +54x+104)} = {16(3 {x}^{2} +22x+7)}}$

$\sf{\Rightarrow30 {x}^{2} +270x+520 = 48 {x}^{2} +352x+112}$

$\sf{\Rightarrow 18 {x}^{2} +82x-408 = 0}$

$\sf{\Longrightarrow{9 {x}^{2} +41x-204 = 0}}$

$\sf{\Rightarrow9 {x}^{2} - 27x + 68x - 204 = 0}$

$\sf{\Rightarrow 9x(x-3)+68(x-3) = 0}$

$\sf{\Longrightarrow (9x+68)(x-3) = 0 }$

$\sf{\Longrightarrow x = \frac{ - 68}{9} \: \: or \: \: 3}$

Answer 2

$\sf \pmb{Answer :}$

Question

$\sf{Solve= \dfrac{12x+17}{3x+1} -\dfrac{ 2x+15}{X+7}=3\dfrac{1}{5}}$

$\sf{Answer \bold{ = -68/9\ \ \ \ or\ \ 3}}$

Step by step explanation:

$\sf{\Rightarrow\dfrac{12x+17}{3x+1} -\dfrac{ 2x+15}{X+7}=\dfrac{16}{5}}$

$\sf{\Rightarrow\dfrac{12x+17}{3x+1} -\dfrac{ 2x+15}{x+7}=\dfrac{16}{5}}$

$\sf{\Rightarrow \dfrac{12x+17}{3x+1} -\dfrac{ 2x+15}{X+7}=\dfrac{16}{5}}$

$\sf{\Rightarrow \frac{((12x+17)(x+7) - (2x+15)(3x+1))}{((x+7)(3x+1))} = \frac{16}{ 5}}$

$\sf{\Rightarrow \frac{(12 {x}^{2} +101x+119-6 {x}^{2} -47x-15)}{(3 {x}^{2} +22x+7)} = \frac{16}{ 5}}$

$\sf{\Rightarrow\frac{(6{x}^{2} +54x+104 )}{(3 {x}^{2} +22x+7)} = \frac{16}{ 5} }$

$\sf{\Rightarrow {5(6 {x}^{2} +54x+104)} = {16(3 {x}^{2} +22x+7)}}$

$\sf{\Rightarrow30 {x}^{2} +270x+520 = 48 {x}^{2} +352x+112}$

$\sf{\Rightarrow 18 {x}^{2} +82x-408 = 0}$

$\sf{\Longrightarrow{9 {x}^{2} +41x-204 = 0}}$

$\sf{\Rightarrow9 {x}^{2} - 27x + 68x - 204 = 0}$

$\sf{\Rightarrow 9x(x-3)+68(x-3) = 0}$

$\sf{\Longrightarrow (9x+68)(x-3) = 0 }$

$\sf{\Longrightarrow x = \frac{ - 68}{9} \: \: or \: \: 3}$