# Problem of the Week

## Updated at May 6, 2019 4:09 PM

To get more practice in equation, we brought you this problem of the week:

How can we solve the equation $$\frac{3}{3-w}+\frac{20}{w}=\frac{5}{2}$$?

Check out the solution below!

$\frac{3}{3-w}+\frac{20}{w}=\frac{5}{2}$

 1 Multiply both sides by the Least Common Denominator: $$2w(3-w)$$.$6w+40(3-w)=5w(3-w)$2 Simplify.$-34w+120=15w-5{w}^{2}$3 Move all terms to one side.$34w-120+15w-5{w}^{2}=0$4 Simplify  $$34w-120+15w-5{w}^{2}$$  to  $$49w-120-5{w}^{2}$$.$49w-120-5{w}^{2}=0$5 Multiply both sides by $$-1$$.$5{w}^{2}-49w+120=0$6 Split the second term in $$5{w}^{2}-49w+120$$ into two terms.1 Multiply the coefficient of the first term by the constant term.$5\times 120=600$2 Ask: Which two numbers add up to $$-49$$ and multiply to $$600$$?$$-24$$ and $$-25$$3 Split $$-49w$$ as the sum of $$-24w$$ and $$-25w$$.$5{w}^{2}-24w-25w+120$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$5{w}^{2}-24w-25w+120=0$7 Factor out common terms in the first two terms, then in the last two terms.$w(5w-24)-5(5w-24)=0$8 Factor out the common term $$5w-24$$.$(5w-24)(w-5)=0$9 Solve for $$w$$.1 Ask: When will $$(5w-24)(w-5)$$ equal zero?When $$5w-24=0$$ or $$w-5=0$$2 Solve each of the 2 equations above.$w=\frac{24}{5},5$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$w=\frac{24}{5},5$Done Decimal Form: 4.8, 5w=24/5,5