Solve 2x/3x-1 - ScanMath

Question

Simplify the expression

\frac{2 x ^{2} - 3}{3}

Evaluate

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

Remove the parentheses

2 \times \frac{x}{3} x - 1

Multiply the terms

More Steps

Multiply the terms

2 \times \frac{x}{3} x

Multiply the terms

\frac{2 x}{3} x

Multiply the terms

\frac{2 x \times x}{3}

Multiply the terms

\frac{2 x ^{2}}{3}

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

Reduce fractions to a common denominator

\frac{2 x ^{2}}{3} - \frac{3}{3}

Solution

\frac{2 x ^{2} - 3}{3}

Show Solution

x_{1} = - \frac{6}{2}, x_{2} = \frac{6}{2}

Alternative Form

x_{1} \approx - 1.224745, x_{2} \approx 1.224745

Evaluate

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

To find the roots of the expression,set the expression equal to 0

(2 \times \frac{x}{3}) x - 1 = 0

Multiply the terms

\frac{2 x}{3} x - 1 = 0

Multiply the terms

More Steps

Multiply the terms

\frac{2 x}{3} x

Multiply the terms

\frac{2 x \times x}{3}

Multiply the terms

\frac{2 x ^{2}}{3}

\frac{2 x ^{2}}{3} - 1 = 0

Subtract the terms

More Steps

Simplify

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

Reduce fractions to a common denominator

\frac{2 x ^{2}}{3} - \frac{3}{3}

Write all numerators above the common denominator

\frac{2 x ^{2} - 3}{3}

\frac{2 x ^{2} - 3}{3} = 0

Simplify

2 x^{2} - 3 = 0

Move the constant to the right side

2 x^{2} = 3

Divide both sides

\frac{2 x ^{2}}{2} = \frac{3}{2}

Divide the numbers

x^{2} = \frac{3}{2}

Take the root of both sides of the equation and remember to use both positive and negative roots

x = \pm \frac{3}{2}

Simplify the expression

More Steps

Evaluate

\frac{3}{2}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{3}{2}

Multiply by the Conjugate

\frac{3 \times 2}{2 \times 2}

Multiply the numbers

More Steps

Evaluate

3 \times 2

The product of roots with the same index is equal to the root of the product

3 \times 2

Calculate the product

6

\frac{6}{2 \times 2}

When a square root of an expression is multiplied by itself,the result is that expression

\frac{6}{2}

x = \pm \frac{6}{2}

Separate the equation into 2 possible cases

x = \frac{6}{2} x = - \frac{6}{2}

Solution

x_{1} = - \frac{6}{2}, x_{2} = \frac{6}{2}

Alternative Form

x_{1} \approx - 1.224745, x_{2} \approx 1.224745

Show Solution