Given the equation:

\[
\frac{\sqrt{y} - 1}{\sqrt{y}} = 2
\]

We will solve for \( y \).

### Step 1: Simplify the left-hand side

Break down the left-hand side into two terms:

\[
\frac{\sqrt{y} - 1}{\sqrt{y}} = \frac{\sqrt{y}}{\sqrt{y}} - \frac{1}{\sqrt{y}} = 1 - \frac{1}{\sqrt{y}}
\]

Now the equation becomes:

\[
1 - \frac{1}{\sqrt{y}} = 2
\]

### Step 2: Isolate the square root term

Subtract 1 from both sides:

\[
- \frac{1}{\sqrt{y}} = 2 - 1
\]

\[
-\frac{1}{\sqrt{y}} = 1
\]

Multiply both sides by -1:

\[
\frac{1}{\sqrt{y}} = -1
\]

### Step 3: Solve for \( y \)

Take the reciprocal of both sides:

\[
\sqrt{y} = -1
\]

Square both sides to remove the square root:

\[
y = (-1)^2 = 1
\]

### Step 4: Verify the solution

Substitute \( y = 1 \) back into the original equation:

\[
\frac{\sqrt{1} - 1}{\sqrt{1}} = \frac{1 - 1}{1} = 0
\]

But this does not satisfy the equation \( 2 \). Hence, there is **no solution** to the given equation.

### Question:

Do you have any more questions or would you like further details?

Here are 5 related questions:
1. How can I solve equations involving square roots and fractions?
2. What if the square root term involves a negative value—how do we handle it?
3.

Explore how to solve equations involving square roots and fractions, specifically for the problem sqrty-1/sqrty=2. This detailed step-by-step solution covers key algebraic concepts and is suitable for students in Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation