If $x+y=2z$,find the value of $\frac{x}{x-z}+\frac{z}{y-z}$.

Solve the given two equations and select the correct answer from the given options.
$I.$ $4x^2 - 43x + 105 = 0$
$II.$ $7y^2 - 29y + 30 = 0$

If $|{x^2} - x - 6| = x + 2$,then the values of $x$ are

If $f(x) = ax^2 + 2bx + c = 0$ has imaginary roots and $4a + 4b + c < 0$,then:

All the pairs $(x, y)$ that satisfy the inequality $2^{\sqrt{\sin^2 x - 2\sin x + 5}} \cdot \frac{1}{4^{\sin^2 y}} \leq 1$ also satisfy the equation:

Solve the given two equations and select the correct option.
$I.$ $7x + 3y = 26$
$II.$ $2x + 17y = -41$