Question

solve the following equation:6x+7/3x+2=4x+13/2x+5​

Answer 1

Answer:

$x+1+4x+13=3x+12</p><p></p><p>squaring both sides</p><p></p><p>⇒x+1+4x+13+2x+14x+13=3x+12</p><p></p><p>⇒2x+13x+13=3x+12−5x−14=−2x−2</p><p></p><p>⇒2x+14x+13=−2(x+1)</p><p></p><p>squaring both sides</p><p></p><p>⇒(x+1)(4x+13)=(x+1)2=x2+1+2x</p><p></p><p>     4x2+4x+13+13x=x2+2x+1</p><p></p><p>     3x2+15x+12=0</p><p></p><p>     x2+5x+4=0</p><p></p><p>     x2+4x+x+4=0</p><p></p><p>     x(x+4)+(x+4)=0</p><p></p><p>     (x+4)+(x+4)=0</p><p></p><p>⇒x=−1,−4</p><p></p><p>Hence, the answer is −1,−4.</p><p></p><p>$

Answer 2

(2x+5) (6x+7) = (4x+13) ( 3x+2) ( cross multiply)

2x(6x+7) + 5(6x+7) = 4x(3x+2)+13(3x+2)

12x²+14x+30x+35 = 12x²+8x+39x+26

12x²-12x²+44x+35 = 47x +26

35-26 = 47x - 44x ( opposite side change sign)

9 = 3x

9/3 =x ( opposite side change sign)

3 = x