# Problem of the Week

## Updated at Jun 6, 2022 2:02 PM

How would you solve $$\frac{(3-\frac{5}{x})(x+2)}{2}=1$$?

Below is the solution.

$\frac{(3-\frac{5}{x})(x+2)}{2}=1$

 1 Multiply both sides by $$2$$.$(3-\frac{5}{x})(x+2)=2$2 Expand.$3x+6-5-\frac{10}{x}=2$3 Simplify  $$3x+6-5-\frac{10}{x}$$  to  $$3x+1-\frac{10}{x}$$.$3x+1-\frac{10}{x}=2$4 Multiply both sides by $$x$$.$3{x}^{2}+x-10=2x$5 Move all terms to one side.$3{x}^{2}+x-10-2x=0$6 Simplify  $$3{x}^{2}+x-10-2x$$  to  $$3{x}^{2}-x-10$$.$3{x}^{2}-x-10=0$7 Split the second term in $$3{x}^{2}-x-10$$ into two terms.1 Multiply the coefficient of the first term by the constant term.$3\times -10=-30$2 Ask: Which two numbers add up to $$-1$$ and multiply to $$-30$$?$$5$$ and $$-6$$3 Split $$-x$$ as the sum of $$5x$$ and $$-6x$$.$3{x}^{2}+5x-6x-10$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$3{x}^{2}+5x-6x-10=0$8 Factor out common terms in the first two terms, then in the last two terms.$x(3x+5)-2(3x+5)=0$9 Factor out the common term $$3x+5$$.$(3x+5)(x-2)=0$10 Solve for $$x$$.1 Ask: When will $$(3x+5)(x-2)$$ equal zero?When $$3x+5=0$$ or $$x-2=0$$2 Solve each of the 2 equations above.$x=-\frac{5}{3},2$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$x=-\frac{5}{3},2$Done Decimal Form: -1.666667, 2x=-5/3,2