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# Algebra

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Find all values of y that satisfy the equation y/3 + 1 = (y + 3)/y + 7.

Feb 14, 2022

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To make the equation clear, it looks like this: $${y\over3}+1={y+3\over y}+7$$.

Then multiply every term by '3y'.

It should now look like this:$$y^2 + 3y = 3y + 9 + 21y$$.

Combining like terms and moving the equation to one side, we get: $$y^2 - 21y - 9 = 0$$.

Then you can use the quadratic formula $$x = {-b \pm \sqrt{b^2-4ac} \over 2a}$$ where a is the coefficient of x^2. b is the coefficient of x, and c is the constant.

Plugging in the values, we have:

$$y = {21 + 3\sqrt{53}\over2}$$

$$y = {21-3\sqrt{53}\over2}$$

Those are the two possible values of y :)

Feb 14, 2022