# Problem of the Week

## Updated at Mar 22, 2021 2:49 PM

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

How would you solve the equation $$\frac{3}{3-{(\frac{5}{m})}^{2}}=\frac{3}{2}$$?

Check out the solution below!

$\frac{3}{3-{(\frac{5}{m})}^{2}}=\frac{3}{2}$

 1 Use Division Distributive Property: $${(\frac{x}{y})}^{a}=\frac{{x}^{a}}{{y}^{a}}$$.$\frac{3}{3-\frac{{5}^{2}}{{m}^{2}}}=\frac{3}{2}$2 Simplify  $${5}^{2}$$  to  $$25$$.$\frac{3}{3-\frac{25}{{m}^{2}}}=\frac{3}{2}$3 Multiply both sides by $$3-\frac{25}{{m}^{2}}$$.$3=\frac{3}{2}(3-\frac{25}{{m}^{2}})$4 Divide both sides by $$3$$.$1=\frac{1}{2}(3-\frac{25}{{m}^{2}})$5 Simplify  $$\frac{3-\frac{25}{{m}^{2}}}{2}$$  to  $$\frac{3}{2}-\frac{\frac{25}{{m}^{2}}}{2}$$.$1=\frac{3}{2}-\frac{\frac{25}{{m}^{2}}}{2}$6 Simplify  $$\frac{\frac{25}{{m}^{2}}}{2}$$  to  $$\frac{25}{2{m}^{2}}$$.$1=\frac{3}{2}-\frac{25}{2{m}^{2}}$7 Subtract $$\frac{3}{2}$$ from both sides.$1-\frac{3}{2}=-\frac{25}{2{m}^{2}}$8 Simplify  $$1-\frac{3}{2}$$  to  $$-\frac{1}{2}$$.$-\frac{1}{2}=-\frac{25}{2{m}^{2}}$9 Multiply both sides by $$2{m}^{2}$$.$-\frac{1}{2}\times 2{m}^{2}=-25$10 Cancel $$2$$.$-{m}^{2}=-25$11 Multiply both sides by $$-1$$.${m}^{2}=25$12 Take the square root of both sides.$m=\pm \sqrt{25}$13 Since $$5\times 5=25$$, the square root of $$25$$ is $$5$$.$m=\pm 5$Done m=5,-5