Multiply each side of the given equation by <span>ax−2</span> (so you can get rid of the fraction). When you multiply each side by ax−2, you should have:
<span><span><span><span>24 x ^2 </span>+ 25x </span>− 47 </span>= <span><span><span>(<span><span>−8x</span>−3</span>)</span><span>(<span>ax−2</span>)</span></span>−53</span></span>
You should then multiply <span>(<span><span>−8x</span>−3</span>)</span> and <span>(<span>ax−2</span>)</span> using FOIL.
<span><span><span><span>24 x ^2 </span>+ 25x </span>− 47</span>= <span><span><span><span><span>−<span>8ax^2 </span></span>− <span>3ax </span></span>+ 16x </span>+ 6 </span>− 53</span></span>
Then, reduce on the right side of the equation
<span><span><span><span>24 x ^2 </span>+ 25x </span>− 47</span>= (<span><span>−<span>8x </span></span>− <span>3(ax - 2) - 53</span></span></span>
Since the coefficients of the x^2-term have to be equal on both sides of the equation, <span><span>−8a</span>=24</span>, or <span>a=−3</span>.
Your answer would be <span>
B</span>
