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**HallsofIvy** Please recall that multiplying both sides of an inequality, like [tex]\frac{a}{b}> 1[tex], by a retains the direction of the inequality only if a is **positive**. If a is negative, the inequality is **reversed**.

Given that $\displaystyle \frac{a}{b}> 0$ and a is positive then $\displaystyle \left(\frac{b}{a}\right)a= b> 0(a)= 0$ so b is also positive. But if a is negative then [tex]\left(\frac{a}{b}\right)a= b< 0(a)= 0[tex]. That is, if $\displaystyle \frac{b}{a}> 0$ then **either** a and b are both positive **or** a and b are both negative.