Solve 1/2+1/2x=x^2-7x+10/4x by re-writing the equation as a proportion. which proportion is equivalent to the original equation?

Rewriting the equation as a proportion, we have
     (1/2 * 2x/2x) + (1/2x * 2/2) = (x^2 - 7x + 10)/4x
     (2x/4x) + (2/4x) = (x^2 - 7x + 10)/4x

Multiplying both sides of the equation by 4x to clear the denominators:
     2x + 2 = x^2 - 7x + 10
We now have a new equation that is equivalent to the original equation:
     x^2 - 9x + 8 = 0

We can also write the equation into its factored form:
     (x - 8)(x - 1) = 0
Now we have a product of two expressions that is equal to zero, which means any x value that makes either (x - 8) or (x - 1) zero will make their product zero.
     x - 8 = 0  => x = 8
     x - 1 = 0  => x = 1
Therefore, our solutions are x = 8 and x = 1.

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