2030 AMC 8 Problems/Problem 1

Problem

The equation is shown as: $\frac{24x^2+25x-47}{ax-2}=-8x-3-\frac{53}{ax-2}$ is true for all values except when $x=\frac{2}{a}$ , where a is constant. What is the value of a?

$\text {(A)}\ -16 \qquad \text {(B)}\ -3 \qquad \text {(C)}\ 0 \qquad \text {(D)}\ 3 \qquad \text {(E)} 16$

Solution 1

The faster way is to multiply each side of the given equation by $𝑎𝑥−2$ (Error compiling LaTeX. Unknown error_msg)

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2030 AMC 8 Problems/Problem 1

Problem

Solution 1

Solution 2