following by rationalizing the denominator and reducing, if necessal \[ \frac{48}{5+\sqrt{13}} \]

Calculate or simplify the expression \( \frac{48}{5+\sqrt{13}} \). Calculate the value by following steps: - step0: Calculate: \(\frac{48}{5+\sqrt{13}}\) - step1: Multiply by the Conjugate: \(\frac{48\left(5-\sqrt{13}\right)}{\left(5+\sqrt{13}\right)\left(5-\sqrt{13}\right)}\) - step2: Multiply the numbers: \(\frac{48\left(5-\sqrt{13}\right)}{12}\) - step3: Factor the expression: \(\frac{4\left(5-\sqrt{13}\right)\times 12}{12}\) - step4: Reduce the fraction: \(4\left(5-\sqrt{13}\right)\) - step5: Apply the distributive property: \(4\times 5-4\sqrt{13}\) - step6: Multiply the numbers: \(20-4\sqrt{13}\) The rationalized form of the given expression \(\frac{48}{5+\sqrt{13}}\) after rationalizing the denominator and reducing is \(20-4\sqrt{13}\).