Question

Solve
1
2
+
1
2x
=
x2 − 7x+10
4x
by rewriting the equation as a proportion.

Which proportion is equivalent to the original equation?


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mc001-2.jpg

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Answer 1

Combine the left-side fractions: 1/2 = x/(2x), so
1/2 + 1/(2x) = (x + 1)/(2x).

Thus the equation becomes the proportion
(x + 1)/(2x) = (x^2 − 7x + 10)/(4x).

(Equivalently, cross-multiplying gives 2(x + 1) = x^2 − 7x + 10, which leads to x = 1 or x = 8.)