Write the following expression as a fraction in its simplest form. (t2 + 4t − 21)/9 × 11/((t−3)(t+13))

Question

ScanSolve AI Tutor · Accepted Answer

Step 1: Factor the quadratic expression in the numerator of the first fraction. We need to find two numbers that multiply to −21 and add to 4. These numbers are 7 and −3. So, t²+4t−21 = (t+7)(t−3). Step 2: Substitute the factored expression back into the original problem. ((t+7)(t−3))/(9) × (11)/((t−3)(t+13)) Step 3: Cancel out the common term (t−3) from the numerator and the denominator. (t+7)(t−3)9 × 11(t−3)(t+13) Step 4: Multiply the remaining terms in the numerator and the denominator. (11(t+7))/(9(t+13)) The fully simplified expression is: (11(t+7))/(9(t+13))

Write the following expression as a fraction in its simplest form. (t2 + 4t - 21)/9 * 11/((t-3)(t+13))

Answer

Step-by-step solution

Factor the quadratic expression in the numerator of the first fraction.

Substitute the factored expression back into the original problem.

Cancel out the common term $(t-3)$ from the numerator and the denominator.

Multiply the remaining terms in the numerator and the denominator.

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