Find all values of u which satifies the equation: 1 u − 2 = − 4 + 5 u + 1

Question

Find all values of u which satifies the equation:      1          u      −      2        =  −  4  +      5          u      +      1

tangouwn · Accepted Answer

we will begin by multiplying the entire problem by
(u-2)(u+1)
when you have completed that you will cancelout the fractionand be left with
u+1=(u+1)(u-2)(-4)+5(u-2)
This will simplify to

u + 1 = (u^{2} - u - 2) (- 4) + 5 u - 10

This in turn will be come your quadratic equation by movingeverything to the left of the equal sign and simplifying we willget

4 u^{2} - 8 u + 3 = 0

From here you can use the quadratic formula to solve for x orin this case u

u = \frac{- (- 8) \pm \sqrt{- 8^{2} - 4 (4) (3)}}{2 (4)}

let us simplify this to

u = \frac{8 \pm \sqrt{64 - 48}}{8}

this becomes

u = \frac{8 \pm \sqrt{16}}{8}

lets start cleaning it up

u = \frac{8 \pm 4}{8}

here we have to routes to take u=12/8, and u=4/8

u = \frac{12}{8}

this reduces to answer 1

u = \frac{3}{2}

for answer 2 we will use

u = \frac{4}{8}

and end up with

u = \frac{1}{2}

u = \frac{1}{2}, u = \frac{3}{2}

all values of u

Find all values of u which satifies the equation: 1/(u-2)=-4+5/(u+1)

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