Question

z+2 / z+5 = z / z+6​

Answer 1

$\sf \red{\frac {z + 2}{z + 5} = \frac{z}{z + 6} }$

$\large\mathsf{(z+2).(z+6) \: = \: z.(z+5)}$

$\large\mathsf{{z}^{2}+8z+12 \: = \: {z}^{2}+5z}$

$\large\mathsf{{z}^{2}-{z}^{2}+8z-5z+12 \: = \: 0}$

$\large\mathsf{3z \: = \: -12}$

$\large\mathsf{z \: = \: \frac{-12}{3}}$

$\large\mathsf{z \: = \: -4}$

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Answer 2

$\huge\boxed{\fcolorbox{red}{yellow}{ANSWER..}}$

z + 2 / z+5 = z / z + 6

( z + 2 )( z + 6 ) = z ( z + 5 )

z² + 8z + 12 = z² + 5z

z² - z² + 8z - 5z + 12 = 0

3z = -12

z = -12/3

z = -4