Solve u=3-2/u - ScanMath

Question

Solve the equation

u_{1} = 1, u_{2} = 2

Evaluate

u = 3 - \frac{2}{u}

Find the domain

u = 3 - \frac{2}{u}, u \neq = 0

Multiply both sides of the equation by LCD

u \times u = (3 - \frac{2}{u}) u

Simplify the equation

u^{2} = (3 - \frac{2}{u}) u

Simplify the equation

More Steps

Evaluate

(3 - \frac{2}{u}) u

Apply the distributive property

3 u - \frac{2}{u} \times u

Simplify

3 u - 2

u^{2} = 3 u - 2

Move the expression to the left side

u^{2} - (3 u - 2) = 0

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

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

Factor the expression

More Steps

Evaluate

u^{2} - 3 u + 2

Rewrite the expression

u^{2} + (- 1 - 2) u + 2

Calculate

u^{2} - u - 2 u + 2

Rewrite the expression

u \times u - u - 2 u + 2

Factor out u from the expression

u (u - 1) - 2 u + 2

Factor out - 2 from the expression

u (u - 1) - 2 (u - 1)

Factor out u - 1 from the expression

(u - 2) (u - 1)

(u - 2) (u - 1) = 0

When the product of factors equals 0,at least one factor is 0

u - 2 = 0 u - 1 = 0

Solve the equation for u

More Steps

Evaluate

u - 2 = 0

Move the constant to the right-hand side and change its sign

u = 0 + 2

Removing 0 doesn't change the value,so remove it from the expression

u = 2

u = 2 u - 1 = 0

Solve the equation for u

More Steps

Evaluate

u - 1 = 0

Move the constant to the right-hand side and change its sign

u = 0 + 1

Removing 0 doesn't change the value,so remove it from the expression

u = 1

u = 2 u = 1

Check if the solution is in the defined range

u = 2 u = 1, u \neq = 0

Find the intersection of the solution and the defined range

u = 2 u = 1

Solution

u_{1} = 1, u_{2} = 2

Show Solution

Solve the equation

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