# How do you combine (x-1)/x-(t+1)/t?

Jul 10, 2016

$- \frac{t + x}{t x}$

#### Explanation:

To combine them you must have a denominator that is divisible by both $t$ and $x$. The most obvious one it $t x$

Consider $\frac{x - 1}{x}$

Multiply by 1 but in the form of $1 = \frac{t}{t}$

$\frac{x - 1}{x} \times \frac{t}{t} = \frac{t \left(x - 1\right)}{t x} = \frac{t x - t}{t x}$

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Consider $\frac{t + 1}{t}$

Multiply by 1 but in the form of $1 = \frac{x}{x}$

$\frac{t + 1}{x} \times \frac{x}{x} = \frac{x \left(t + 1\right)}{t x} = \frac{t x + x}{t x}$

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Putting it all together

$\frac{t x - t}{t x} - \frac{t x + x}{t x} \text{ " =" } \frac{\cancel{t x} - t - \cancel{t x} - x}{t x}$

$\frac{- t - x}{t x} \text{ " =" " (-(t+x))/(tx)" " =" } - \frac{t + x}{t x}$