## To solve the equation (27/x) = (8 - 5/x), we can start by cross-multiplying:

27/x = (8 - 5/x)

27(x) = x(8 - 5/x)

Now distribute x on the right side:

27x = 8x - 5

Combine like terms by subtracting 8x from both sides:

27x - 8x = -5

Simplify the left side:

19x = -5

Divide both sides by 19 to isolate x:

x = -5/19

4) To simplify the expression (7m^7n^4/8m) divided by (9m^2n^9/5n^2), we can simplify both the numerator and denominator separately, and then divide:

Numerator simplification:

7m^7n^4 / 8m

Divide both the coefficients and subtract the exponents of m:

7/8 * m^7/m

Simplify:

7m^6 / 8

Denominator simplification:

9m^2n^9 / 5n^2

Divide both the coefficients and subtract the exponents of m and n:

9/5 * m^2/m^0 * n^9/n^2

Since any value raised to the power of 0 is 1, we have:

9/5 * m^2 * n^7

Now, divide the numerator by the denominator:

(7m^6 / 8) / (9/5 * m^2 * n^7)

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction:

(7m^6 / 8) * (5/9 * 1/m^2 * 1/n^7)

Simplify the coefficients and combine the like terms with the same bases:

35m^6 / 72mn^7