Final answer:
The expression x²/(x²x - 42) seems to have a typo and should probably read x²/(x³ - 42). To decompose it into partial fractions, one would normally factor the denominator and divide the original fraction into simpler fractions. Due to the complexity of factoring x³ - 42, alternative methods might be required.
Step-by-step explanation:
The given expression appears to be missing its partial fraction decomposition. To explain the complete question for the fraction decomposition of the expression x²/(x²x - 42), there's a typo that needs to be corrected. Assuming the expression should read x²/(x³ - 42), you'd decompose the cubic denominator into linear and quadratic factors, if possible. However, in this case, the cubic term does not factor nicely over the integers.
For expressions that can be factored, the technique involves expressing the rational function as a sum of simpler fractions, the denominators of which are the factors of the original denominator, and finding the numerators which make the equation true. As this example cannot be factored easily, alternative methods such as long division might be needed if x³ - 42 does not have rational roots or is irreducible.