Question

solve:
\frac{k}{k + 5} + \frac{5}{7 - k} = 1

k = ?

Explanation:

Step1: Eliminate denominators

Multiply all terms by $(k+5)(7-k)$:
$$k(7-k) + 5(k+5) = 1 \cdot (k+5)(7-k)$$

Step2: Expand all expressions

$$7k - k^2 + 5k + 25 = -k^2 + 2k + 35$$

Step3: Simplify left side

Combine like terms:
$$-k^2 + 12k + 25 = -k^2 + 2k + 35$$

Step4: Cancel $-k^2$ from both sides

$$12k + 25 = 2k + 35$$

Step5: Isolate variable terms

Subtract $2k$ from both sides:
$$10k + 25 = 35$$

Step6: Isolate constant terms

Subtract 25 from both sides:
$$10k = 10$$

Step7: Solve for $k$

Divide by 10:
$$k = \frac{10}{10} = 1$$

Answer:

$k = 1$