# Problem of the Week

## Updated at Nov 4, 2019 9:16 AM

For this week we've brought you this equation problem.

How would you solve the equation $$\frac{2+\frac{5}{x}}{4(x+2)}=\frac{9}{32}$$?

Here are the steps:

$\frac{2+\frac{5}{x}}{4(x+2)}=\frac{9}{32}$

 1 Multiply both sides by $$4(x+2)$$.$2+\frac{5}{x}=\frac{9}{32}\times 4(x+2)$2 Use this rule: $$\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}$$.$2+\frac{5}{x}=\frac{9\times 4(x+2)}{32}$3 Simplify  $$9\times 4(x+2)$$  to  $$36(x+2)$$.$2+\frac{5}{x}=\frac{36(x+2)}{32}$4 Simplify  $$\frac{36(x+2)}{32}$$  to  $$\frac{9(x+2)}{8}$$.$2+\frac{5}{x}=\frac{9(x+2)}{8}$5 Multiply both sides by the Least Common Denominator: $$8x$$.$16x+40=9x(x+2)$6 Simplify.$16x+40=9{x}^{2}+18x$7 Move all terms to one side.$16x+40-9{x}^{2}-18x=0$8 Simplify  $$16x+40-9{x}^{2}-18x$$  to  $$-2x+40-9{x}^{2}$$.$-2x+40-9{x}^{2}=0$9 Multiply both sides by $$-1$$.$9{x}^{2}+2x-40=0$10 Split the second term in $$9{x}^{2}+2x-40$$ into two terms.1 Multiply the coefficient of the first term by the constant term.$9\times -40=-360$2 Ask: Which two numbers add up to $$2$$ and multiply to $$-360$$?$$20$$ and $$-18$$3 Split $$2x$$ as the sum of $$20x$$ and $$-18x$$.$9{x}^{2}+20x-18x-40$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$9{x}^{2}+20x-18x-40=0$11 Factor out common terms in the first two terms, then in the last two terms.$x(9x+20)-2(9x+20)=0$12 Factor out the common term $$9x+20$$.$(9x+20)(x-2)=0$13 Solve for $$x$$.1 Ask: When will $$(9x+20)(x-2)$$ equal zero?When $$9x+20=0$$ or $$x-2=0$$2 Solve each of the 2 equations above.$x=-\frac{20}{9},2$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$x=-\frac{20}{9},2$Done Decimal Form: -2.222222, 2x=-20/9,2