type the correct answer in each box. solve the equation, and enter the solutions from least to greatest. if…

Explanation:

Step1: Find common denominator

The common denominator of the left - hand side is $x(x - 10)$. So we rewrite the left - hand side as $\frac{x-10+x}{x(x - 10)}=\frac{2x - 10}{x(x - 10)}$. The right - hand side is $\frac{x - 9}{x - 10}$.

Step2: Cross - multiply

Since $\frac{2x - 10}{x(x - 10)}=\frac{x - 9}{x - 10}$, cross - multiplying gives $(2x - 10)(x - 10)=x(x - 9)(x - 10)$ (note $x\neq10$). Canceling out $(x - 10)$ on both sides (for $x\neq10$), we get $2x-10=x(x - 9)$.

Step3: Expand and rearrange

Expand $2x-10=x^2-9x$ to $x^2-9x-2x + 10=0$, which simplifies to $x^2-11x + 10=0$.

Step4: Factor the quadratic equation

Factor $x^2-11x + 10$ as $(x - 1)(x - 10)=0$.

Step5: Solve for x

Setting each factor equal to zero gives $x-1=0$ or $x - 10=0$. But $x = 10$ is an extraneous solution (because it makes the original denominators zero). So $x=1$.

Answer:

$x = 1$ or $x=n.a.$