Question

Solve the equation z / z-5 + 1/3 = -5 /5-z

Answer 1

$\frac{z}{z - 5} + \frac{1}{3} = \frac{ - 5}{5 - z}$

$\frac{3z}{3z - 15} + \frac{z - 5}{3z - 15} = \frac{ - 5}{5 - z}$

$\frac{4z - 5}{3z - 15} = \frac{ - 5}{5 - z}$

$(4z - 5)(5 - z) = ( - 5)(3z - 15)$

$20z - 4{z}^{2} - 25 + 5z = - 15z + 75$

$4 {z}^{2} - 25z + 25 = 15z - 75$

$4 {z}^{2} - 40z + 100 = 0$

${z}^{2} - 10z + 25 = 0$

${z}^{2} - 5z - 5z + 25 = 0$

$z(z - 5) - 5(z - 5) = 0$

$(z - 5)(z - 5) = 0$

$z - 5 = 0$

$z = 5$

Hope this helps.

Thanks.