Simplify the left side.<span><span>−<span><span>y<span>−2</span></span><span>4y</span></span></span>=<span><span>y<span>−9</span></span><span>10y</span></span></span>Remove parentheses.<span><span>−<span><span>y<span>−2</span></span><span>4y</span></span></span>=<span><span>y<span>−9</span></span><span>10y</span></span></span>Set up the rational expression with the same denominator over the entire equation.<span><span>−<span><span><span>5y</span><span>−10</span></span><span>20y</span></span></span>=<span><span><span>2y</span><span>−18</span></span><span>20y</span></span></span>Since the expression on each side of the equation has the same denominator, the numerators must be equal.<span><span>−<span>(<span><span>5y</span><span>−10</span></span>)</span></span>=<span><span>2y</span><span>−18</span></span></span>Simplify the left side<span><span><span><span>−5</span>y</span>+10</span>=<span><span>2y</span><span>−18</span></span></span>Move all terms containing y to the left side of the equation<span><span><span><span>−7</span>y</span>+10</span>=<span>−18</span></span>Move all terms not containing y to the right side of the equation.<span><span><span>−7</span>y</span>=<span>−28</span></span>Divide each term by <span>−7</span> and simplify.<span>y=4</span>Check that all solutions found are valid and are part of the domain by substituting them into the original equation.<span>y=<span>4</span></span>
