Questions: 3 2x^2 / (3x^2 - 4x)

△ Simplify the expression \(3 + \frac{2x^2}{3x^2 - 4x}\). ○ Factor the denominator ▷ Factor out \(x\) from the denominator to simplify the fraction. ☼ The expression becomes \(3 + \frac{2x}{3x - 4}\) after factoring \(x\) from \(3x^2 - 4x\). ○ Combine terms with a common denominator ▷ Rewrite 3 with the common denominator \(3x - 4\) to combine terms. ☼ The expression is rewritten as \(\frac{3(3x - 4)}{3x - 4} + \frac{2x}{3x - 4}\). ○ Simplify the combined expression ▷ Combine the numerators over the common denominator. ☼ The simplified expression is \(\frac{11x - 12}{3x - 4}\). ✧ The simplified expression is \(\frac{11x - 12}{3x - 4}\).

△ Simplify the expression \(3 \cdot \frac{2x^2}{3x^2 - 4x}\). ○ Factor the denominator ▷ Factor out \(x\) from the denominator to simplify the fraction. ☼ The expression becomes \(3 \cdot \frac{2x}{3x - 4}\) after factoring \(x\) from \(3x^2 - 4x\). ○ Simplify the expression ▷ Multiply the simplified fraction by 3. ☼ The simplified expression is \(\frac{6x}{3x - 4}\). ✧ The simplified expression is \(\frac{6x}{3x - 4}\). ☺ $\frac{11x - 12}{3x - 4}$