b. \( \frac{24}{7 m}+14=\frac{10}{m} \)

To solve the equation \( \frac{24}{7 m}+14=\frac{10}{m} \), let's first eliminate the fractions by multiplying both sides by \( 7m \) (the least common multiple of the denominators). This gives us: \[ 24 + 14 \cdot 7m = 70 \] Now, simplifying this: \[ 24 + 98m = 70 \] Next, we subtract 24 from both sides: \[ 98m = 46 \] Finally, we divide by 98: \[ m = \frac{46}{98} = \frac{23}{49} \] So, \( m = \frac{23}{49} \). Now, onto more knowledge about this topic: Equations involving fractions can appear daunting, but they showcase the elegance of algebraic manipulation! By eliminating fractions right away, you simplify the problem significantly. Remember, finding a common denominator is your ally; it keeps the rest of your calculations tidy and straightforward. Practical applications of solving equations like these are vast! In finance, for instance, you might encounter scenarios involving rates and returns that require you to balance formulas to determine break-even points or investment returns. Being able to manipulate equations smoothly could save you a lot of time and money!