Fraction Expressions
1. The problem shows two expressions with fractions and variables $t$ and $x$ nearby. The expressions are:
$$\frac{3+1}{1-1}x$$
$$\frac{3+1}{2-1}x$$
2. Simplify the numerators and denominators step-by-step:
For the first fraction:
Numerator: $3+1=4$
Denominator: $1-1=0$
So, the fraction is $\frac{4}{0}$ which is undefined because division by zero is not allowed.
For the second fraction:
Numerator: $3+1=4$
Denominator: $2-1=1$
So, the fraction is $\frac{4}{1}=4$
3. Now multiply by $x$:
First expression: undefined $\times x$ is still undefined.
Second expression: $4 \times x = 4x$
4. Final answer:
- The first expression is undefined because the denominator is zero.
- The second expression simplifies to $4x$.
Therefore, the only defined and simplified expression is $4x$.