Solve the following equations :
`(x-1)/(7x-14)=(x-3)/(7x-26)`

Answer

To solve the equation \(\frac{x-1}{7x-14}=\frac{x-3}{7x-26}\), we will use cross multiplication. Here are the steps:

### Step 1: Cross Multiply
We start by cross multiplying the two fractions:
\[ (x - 1)(7x - 26) = (x - 3)(7x - 14) \]

### Step 2: Expand Both Sides
Now, we will expand both sides of the equation.
- Left side:
\[ (x - 1)(7x - 26) = 7x^2 - 26x - 7x + 26 = 7x^2 - 33x + 26 \]
- Right side:
\[ (x - 3)(7x - 14) = 7x^2 - 14x - 21x + 42 = 7x^2 - 35x + 42 \]

### Step 3: Set the Equation
Now we have:
\[ 7x^2 - 33x + 26 = 7x^2 - 35x + 42 \]

### Step 4: Simplify
Next, we can subtract \(7x^2\) from both sides:
\[ -33x + 26 = -35x + 42 \]

### Step 5: Rearrange the Equation
Now, let's move all \(x\) terms to one side and constant terms to the other side:
\[ -33x + 35x = 42 - 26 \]
This simplifies to:
\[ 2x = 16 \]

### Step 6: Solve for \(x\)
Now, divide both sides by 2:
\[ x = \frac{16}{2} = 8 \]

### Final Answer
Thus, the solution to the equation is:
\[ \boxed{8} \]

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