Video: Solving Simple Rational Equations with Zero on One Side

Video Transcript

Find 𝑥 given that 𝑥 minus 20 over 𝑥 plus 10 equals zero.

We can solve this problem algebraically by isolating our 𝑥-value. To isolate our 𝑥-value, we’ll need to get this 𝑥 plus 10 out of the denominator. We can get 𝑥 plus 10 out of the denominator by multiplying by the reciprocal on both sides of the equation. 𝑥 plus 10 over 𝑥 plus 10 equals one. These values cancel each other out, leaving us with only 𝑥 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 𝑥 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 𝑥 minus 20 equals zero. We add 20 to both sides of our equation. And we find that 𝑥 equals 20 is a solution to this equation.