Solve \frac{x^2}{4}-\frac{x-1}{3}=2

Question

Solve the equation

x_{1} = - 2, x_{2} = \frac{10}{3}

Alternative Form

x_{1} = - 2, x_{2} = 3. \dot{3}

Evaluate

\frac{x ^{2}}{4} - \frac{x - 1}{3} = 2

Multiply both sides of the equation by LCD

(\frac{x ^{2}}{4} - \frac{x - 1}{3}) \times 12 = 2 \times 12

Simplify the equation

More Steps

Evaluate

(\frac{x ^{2}}{4} - \frac{x - 1}{3}) \times 12

Apply the distributive property

\frac{x ^{2}}{4} \times 12 - \frac{x - 1}{3} \times 12

Simplify

x^{2} \times 3 + (- x + 1) \times 4

Use the commutative property to reorder the terms

3 x^{2} + (- x + 1) \times 4

Multiply the terms

More Steps

Evaluate

(- x + 1) \times 4

Apply the distributive property

- x \times 4 + 1 \times 4

Use the commutative property to reorder the terms

- 4 x + 1 \times 4

Any expression multiplied by 1 remains the same

- 4 x + 4

3 x^{2} - 4 x + 4

3 x^{2} - 4 x + 4 = 2 \times 12

Simplify the equation

3 x^{2} - 4 x + 4 = 24

Move the expression to the left side

3 x^{2} - 4 x + 4 - 24 = 0

Subtract the numbers

3 x^{2} - 4 x - 20 = 0

Factor the expression

More Steps

Evaluate

3 x^{2} - 4 x - 20

Rewrite the expression

3 x^{2} + (- 10 + 6) x - 20

Calculate

3 x^{2} - 10 x + 6 x - 20

Rewrite the expression

x \times 3 x - x \times 10 + 2 \times 3 x - 2 \times 10

Factor out x from the expression

x (3 x - 10) + 2 \times 3 x - 2 \times 10

Factor out 2 from the expression

x (3 x - 10) + 2 (3 x - 10)

Factor out 3 x - 10 from the expression

(x + 2) (3 x - 10)

(x + 2) (3 x - 10) = 0

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

x + 2 = 0 3 x - 10 = 0

Solve the equation for x

More Steps

Evaluate

x + 2 = 0

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

x = 0 - 2

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

x = - 2

x = - 2 3 x - 10 = 0

Solve the equation for x

More Steps

Evaluate

3 x - 10 = 0

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

3 x = 0 + 10

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

3 x = 10

Divide both sides

\frac{3 x}{3} = \frac{10}{3}

Divide the numbers

x = \frac{10}{3}

x = - 2 x = \frac{10}{3}

Solution

x_{1} = - 2, x_{2} = \frac{10}{3}

Alternative Form

x_{1} = - 2, x_{2} = 3. \dot{3}

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