Simplify \( \frac{6+\frac{8}{e^{2}}}{1+\frac{2}{c}} \)

Calculate or simplify the expression \( (6+\frac{8}{e^{2}})/(1+\frac{2}{c}) \). Simplify the expression by following steps: - step0: Solution: \(\frac{\left(6+\frac{8}{e^{2}}\right)}{\left(1+\frac{2}{c}\right)}\) - step1: Remove the parentheses: \(\frac{6+\frac{8}{e^{2}}}{1+\frac{2}{c}}\) - step2: Add the numbers: \(\frac{\frac{6e^{2}+8}{e^{2}}}{1+\frac{2}{c}}\) - step3: Add the terms: \(\frac{\frac{6e^{2}+8}{e^{2}}}{\frac{c+2}{c}}\) - step4: Multiply by the reciprocal: \(\frac{6e^{2}+8}{e^{2}}\times \frac{c}{c+2}\) - step5: Multiply the terms: \(\frac{\left(6e^{2}+8\right)c}{e^{2}\left(c+2\right)}\) - step6: Simplify: \(\frac{\left(6e^{2}+8\right)c}{e^{2}c+2e^{2}}\) - step7: Expand the expression: \(\frac{6e^{2}c+8c}{e^{2}c+2e^{2}}\) The simplified form of the expression \( \frac{6+\frac{8}{e^{2}}}{1+\frac{2}{c}} \) is \( \frac{6e^{2}c+8c}{e^{2}c+2e^{2}} \).