Question

$$\frac{-7x^{\frac{7}{8}}}{-6x^{\frac{3}{8}}}$$

Explanation:

Step1: Cross - multiply

Given the equation \(\frac{-7x-\frac{7}{8}}{-6x-\frac{3}{8}}\), we cross - multiply to get \((-7x-\frac{7}{8})\times1=(-6x - \frac{3}{8})\times1\)? Wait, no, actually, if we assume the equation is \(\frac{-7x-\frac{7}{8}}{-6x-\frac{3}{8}} = 1\)? Wait, maybe the original equation is \(\frac{-7x-\frac{7}{8}}{-6x-\frac{3}{8}}\) and we want to solve for \(x\). Let's rewrite the equation as \(-7x-\frac{7}{8}=-6x-\frac{3}{8}\) (by cross - multiplying, assuming the two sides are equal, maybe it's a proportion like \(\frac{-7x-\frac{7}{8}}{-6x-\frac{3}{8}} = 1\) or some other equality. Let's proceed with solving \(-7x-\frac{7}{8}=-6x-\frac{3}{8}\))

Step2: Move terms with x to one side

Add \(7x\) to both sides: \(-\frac{7}{8}=x-\frac{3}{8}\)

Step3: Solve for x

Add \(\frac{3}{8}\) to both sides: \(x=-\frac{7}{8}+\frac{3}{8}=-\frac{4}{8}=-\frac{1}{2}\)

Wait, maybe the original equation is \(\frac{-7x-\frac{7}{8}}{-6x-\frac{3}{8}}\) and we made a wrong assumption. Let's re - examine the problem. If the equation is \(\frac{-7x-\frac{7}{8}}{-6x-\frac{3}{8}}\) and we want to simplify or solve. Let's factor numerator and denominator:

Numerator: \(-7x-\frac{7}{8}=-7(x + \frac{1}{8})\)

Denominator: \(-6x-\frac{3}{8}=-3(2x+\frac{1}{8})\)

But if we assume it's an equation like \(\frac{-7x-\frac{7}{8}}{-6x-\frac{3}{8}} = \frac{7}{6}\) (maybe a typo or miswriting). Wait, the original image shows \(\frac{-7x^{\frac{7}{8}}}{-6x^{\frac{3}{8}}}\)? No, the original image has \(-7x^{\frac{7}{8}}\) over \(-6x^{\frac{3}{8}}\). Oh! Maybe it's a monomial division: \(\frac{-7x^{\frac{7}{8}}}{-6x^{\frac{3}{8}}}\)

Step1: Simplify the coefficients and exponents

For the coefficient: \(\frac{-7}{-6}=\frac{7}{6}\)

For the variable part: \(x^{\frac{7}{8}-\frac{3}{8}}=x^{\frac{4}{8}}=x^{\frac{1}{2}}=\sqrt{x}\)

So the simplified form is \(\frac{7}{6}\sqrt{x}\) or \(\frac{7}{6}x^{\frac{1}{2}}\)

Assuming the problem is to simplify \(\frac{-7x^{\frac{7}{8}}}{-6x^{\frac{3}{8}}}\)

Step1: Divide the coefficients

The coefficient of the numerator is \(-7\) and the coefficient of the denominator is \(-6\). When we divide \(\frac{-7}{-6}=\frac{7}{6}\)

Step2: Divide the variable terms

Using the rule of exponents \(a^{m}\div a^{n}=a^{m - n}\), for \(x^{\frac{7}{8}}\div x^{\frac{3}{8}}\), we have \(x^{\frac{7}{8}-\frac{3}{8}}=x^{\frac{4}{8}}=x^{\frac{1}{2}}\)

Step3: Combine the results

Multiply the coefficient result and the variable result: \(\frac{7}{6}\times x^{\frac{1}{2}}=\frac{7}{6}\sqrt{x}\) (or \(\frac{7}{6}x^{\frac{1}{2}}\))

Since the original problem's image is a fraction with \(-7x^{\frac{7}{8}}\) (maybe \(x\) with exponent \(\frac{7}{8}\)) over \(-6x^{\frac{3}{8}}\) ( \(x\) with exponent \(\frac{3}{8}\)), the correct simplification is as above.

Answer:

If simplifying \(\frac{-7x^{\frac{7}{8}}}{-6x^{\frac{3}{8}}}\), the result is \(\frac{7}{6}x^{\frac{1}{2}}\) (or \(\frac{7}{6}\sqrt{x}\))