How do you solve the rational equation $\frac{y + 2}{y} = \frac{1}{y - 5}$ $(y+2)/y = 1/(y-5)$ ?

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Answer 1 · 2018-05-20T00:23:42

$y = 2 \pm \sqrt{14}$ $y=2+-sqrt14$

$\frac{y + 2}{y} = \frac{1}{y - 5}$ $(y+2)/y = 1/(y-5)$

$(y + 2) (y - 5) = y$ $(y+2)(y-5) = y$

$y^{2} - 3 y - 10 = y$ $y^2-3y-10=y$

$y^{2} - 4 y - 10 = 0$ $y^2-4y-10=0$

$y = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$ $y=(-b+-sqrt(b^2-4ac))/(2a)$

$y = \frac{4 \pm \sqrt{{(- 4)}^{2} - 4 (1) (- 10)}}{2 \times 1}$ $y=(4+-sqrt((-4)^2-4(1)(-10)))/(2times1)$

$y = \frac{4 \pm \sqrt{16 + 40}}{2}$ $y=(4+-sqrt(16+40))/2$

$y = \frac{4 \pm \sqrt{56}}{2}$ $y=(4+-sqrt56)/2$

$y = \frac{4 \pm 2 \sqrt{14}}{2}$ $y=(4+-2sqrt14)/2$

$y = 2 \pm \sqrt{14}$ $y=2+-sqrt14$

How do you solve the rational equation y+2y=1y−5(y+2)/y = 1/(y-5)?