Achieve_Math_Public Test Spec
\( 5 / 39 \)
\( 125 \% \)
ITED ARAB EMIRATES
VSTRY OF EDUCATION
EmSAT Achieve Math
Public Test Specification
pendix 2: Sample Items
Solve for \( \mathrm{x} \).
\[
\frac{2}{x+3}-\frac{3}{4-x}=\frac{2 x-2}{x^{2}-x-12}
\]
Answer
\begin{aligned} &\frac{2}{x+3}-\frac{3}{4-x}=\frac{2 x-2}{x^{2}-x-12}\\ &\Rightarrow (2)(4 - x) - (3)(x + 3) = (2x - 2)(x^{2} - x - 12)\\ &\Rightarrow 8 - 2x - 3x - 9 = (2x - 2)[(x - 4)(x + 3)]\\ &\Rightarrow -5x - 1 = (2x - 2)(x^{2} - x -12)\\ &\Rightarrow 5x + 1 = (2x - 2)(x^{2} - x - 12)\\ &\Rightarrow 5x +1 = (2x - 2)(x - 4)(x + 3)\\ &\Rightarrow \frac{5x + 1}{2x - 2} = (x-4)(x+3)\\ &\Rightarrow x = 5.6667 \end{aligned}
Step 1 ：\( \frac{5}{39} = \frac{5 \div 5}{39 \div 5} = \frac{1}{7.8} \)
Step 2 ：\( 125 \% = \frac{125}{100} = 1.25 \)
Step 3 ：\begin{aligned} &\frac{2}{x+3}-\frac{3}{4-x}=\frac{2 x-2}{x^{2}-x-12}\\ &\Rightarrow (2)(4 - x) - (3)(x + 3) = (2x - 2)(x^{2} - x - 12)\\ &\Rightarrow 8 - 2x - 3x - 9 = (2x - 2)[(x - 4)(x + 3)]\\ &\Rightarrow -5x - 1 = (2x - 2)(x^{2} - x -12)\\ &\Rightarrow 5x + 1 = (2x - 2)(x^{2} - x - 12)\\ &\Rightarrow 5x +1 = (2x - 2)(x - 4)(x + 3)\\ &\Rightarrow \frac{5x + 1}{2x - 2} = (x-4)(x+3)\\ &\Rightarrow x = 5.6667 \end{aligned}
