Video: Solving Simple Rational Equations with Zero on One Side

Find π‘₯ given that (π‘₯ βˆ’ 20)/(π‘₯ + 10) = 0.

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Video Transcript

Find π‘₯ given that π‘₯ minus 20 over π‘₯ plus 10 equals zero.

We can solve this problem algebraically by isolating our π‘₯-value. To isolate our π‘₯-value, we’ll need to get this π‘₯ plus 10 out of the denominator. We can get π‘₯ plus 10 out of the denominator by multiplying by the reciprocal on both sides of the equation. π‘₯ plus 10 over π‘₯ plus 10 equals one. These values cancel each other out, leaving us with only π‘₯ minus 20 on the left side of the equation.

But something really interesting is also happening on the right side of the equation. We’re multiplying zero times π‘₯ plus 10. This means that our variable on the right side of the equation disappears and we’re left with only zero. Now, we have an equation that says π‘₯ minus 20 equals zero. We add 20 to both sides of our equation. And we find that π‘₯ equals 20 is a solution to this equation.

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