Can you do in cross multiplication method 

Certainly! Let's solve the equation using the cross-multiplication method.

The equation is:

\[
x + \frac{1}{x} = \frac{25}{12}
\]

To eliminate the fraction on the left side, we'll multiply both sides of the equation by \( x \):

\[
x \times x + x \times \frac{1}{x} = x \times \frac{25}{12}
\]

This simplifies to:

\[
x^2 + 1 = \frac{25x}{12}
\]

Now, we'll use cross multiplication to get rid of the fraction. Multiply both sides by 12:

\[
12(x^2 + 1) = 25x
\]

Expand the left side:

\[
12x^2 + 12 = 25x
\]

Next, rearrange the equation to bring all terms to one side:

\[
12x^2 - 25x + 12 = 0
\]

Now, you have a quadratic equation. We can factor this quadratic equation directly (if it can be factored) or use the quadratic formula as before.

Let's try factoring it first:

We look for two numbers that multiply to \( 12 \times 12 = 144 \) and add to \(-25\). The numbers that work are \(-16\) and \(-9\).

Thus, we can factor the quadratic as:

\[
12x^2 - 16x - 9x + 12 = 0
\]

Group the terms:

\[
(12x^2 - 16x) - (9x - 12) = 0
\]

Factor each group:

\[
4x(3x - 4) - 3(3x - 4) = 0
\]

Now, factor out the common binomial factor \( (3x - 4) \):

\[
(4x - 3)(3x - 4) = 0
\]

This gives us two possible solutions:

1. \( 4x - 3 = 0 \) implies \( x = \frac{3}{4} \)
2. \( 3x - 4 = 0 \) implies \( x = \frac{4}{3} \)

So, the two possible values for \( x \) are \( \frac{3}{4} \) and \( \frac{4}{3} \), which match our earlier results.

Would you like to explore any other methods or have any questions?

Here are 5 related questions:
1. Can you solve other quadratic equations using cross multiplication?
2. How do you determine whether a quadratic equation can be factored easily?
3. What are the advantages of using cross multiplication for solving equations?
4. How do you check if your factored form is correct?
5. What are some real-world applications of solving quadratic equations?

**Tip:** Cross multiplication is a powerful technique, especially when dealing with fractions in equations. It simplifies the process by eliminating the fractions early on.

Learn how to solve equations using the cross multiplication method with a detailed step-by-step guide. This problem focuses on quadratic equations and the application of cross multiplication to eliminate fractions. Suitable for high school students studying algebra and quadratic equations.

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