how to so solve this [tex] \frac{3}{x - 7?} \div \frac{x + 5}{x - 7} \times 2[/tex]can you show it step by step
Answer (1)
Answer:The expression you provided is: $ \frac{3}{x-7} \div \frac{x+5}{x-7} \times 2 $ To solve this step-by-step: Step 1: Convert division to multiplication Remember that dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of \frac{x+5}{x-7} is \frac{x-7}{x+5}. Therefore, the expression becomes: $ \frac{3}{x-7} \times \frac{x-7}{x+5} \times 2 $ Step 2: Simplify Notice that (x-7) appears in both the numerator and the denominator. We can cancel them out, provided x \neq 7 (because division by zero is undefined). This simplifies the expression to: $ \frac{3}{1} \times \frac{1}{x+5} \times 2 $ Step 3: Multiply Now, multiply the numerators together and the denominators together: $ \frac{3 \times 1 \times 2}{1 \times (x+5)} = \frac{6}{x+5} $ Step 4: State the final answer and any restrictions The simplified expression is \frac{6}{x+5}. Remember that this is only valid if x \neq 7 and x \neq -5 (to avoid division by zero).
