6. Simplify the ff. (a) \( \frac{x}{4}+\frac{3}{7} \) b) \( \frac{2 x}{4+x}+\frac{x}{3} \) (3) \( \frac{a+1}{b} \times \frac{b^{2}}{a^{2}-1} \)

Calculate or simplify the expression \( (x/4)+(3/7) \). Simplify the expression by following steps: - step0: Solution: \(\frac{x}{4}+\frac{3}{7}\) - step1: Reduce fractions to a common denominator: \(\frac{x\times 7}{4\times 7}+\frac{3\times 4}{7\times 4}\) - step2: Multiply the numbers: \(\frac{x\times 7}{28}+\frac{3\times 4}{7\times 4}\) - step3: Multiply the numbers: \(\frac{x\times 7}{28}+\frac{3\times 4}{28}\) - step4: Transform the expression: \(\frac{x\times 7+3\times 4}{28}\) - step5: Reorder the terms: \(\frac{7x+3\times 4}{28}\) - step6: Multiply the numbers: \(\frac{7x+12}{28}\) Calculate or simplify the expression \( (2*x/(4+x))+(x/3) \). Simplify the expression by following steps: - step0: Solution: \(\left(\frac{2x}{\left(4+x\right)}\right)+\frac{x}{3}\) - step1: Remove the parentheses: \(\left(\frac{2x}{4+x}\right)+\frac{x}{3}\) - step2: Remove the parentheses: \(\frac{2x}{4+x}+\frac{x}{3}\) - step3: Reduce fractions to a common denominator: \(\frac{2x\times 3}{\left(4+x\right)\times 3}+\frac{x\left(4+x\right)}{3\left(4+x\right)}\) - step4: Reorder the terms: \(\frac{2x\times 3}{3\left(4+x\right)}+\frac{x\left(4+x\right)}{3\left(4+x\right)}\) - step5: Transform the expression: \(\frac{2x\times 3+x\left(4+x\right)}{3\left(4+x\right)}\) - step6: Multiply the terms: \(\frac{6x+x\left(4+x\right)}{3\left(4+x\right)}\) - step7: Multiply the terms: \(\frac{6x+4x+x^{2}}{3\left(4+x\right)}\) - step8: Add the terms: \(\frac{10x+x^{2}}{3\left(4+x\right)}\) - step9: Simplify: \(\frac{10x+x^{2}}{12+3x}\) Calculate or simplify the expression \( ((a+1)/b)*((b^2)/(a^2-1)) \). Simplify the expression by following steps: - step0: Solution: \(\left(\frac{\left(a+1\right)}{b}\right)\left(\frac{b^{2}}{\left(a^{2}-1\right)}\right)\) - step1: Remove the parentheses: \(\left(\frac{a+1}{b}\right)\left(\frac{b^{2}}{a^{2}-1}\right)\) - step2: Remove the parentheses: \(\frac{a+1}{b}\times \left(\frac{b^{2}}{a^{2}-1}\right)\) - step3: Remove the parentheses: \(\frac{a+1}{b}\times \frac{b^{2}}{a^{2}-1}\) - step4: Rewrite the expression: \(\frac{a+1}{b}\times \frac{b^{2}}{\left(a+1\right)\left(a-1\right)}\) - step5: Reduce the fraction: \(1\times \frac{b}{a-1}\) - step6: Multiply the terms: \(\frac{b}{a-1}\) The simplified expressions are: a) \( \frac{x}{4}+\frac{3}{7} = \frac{7x+12}{28} \) b) \( \frac{2x}{4+x}+\frac{x}{3} = \frac{10x+x^{2}}{12+3x} \) c) \( \frac{a+1}{b} \times \frac{b^{2}}{a^{2}-1} = \frac{b}{a-1} \)