Final Answer:
The decomposition of the fraction x² + x² + x - 42 involves factoring the expression to simplify it. However, as the expression x² + x² + x - 42 doesn't represent a fraction, decomposition in terms of factoring or partial fractions seems unnecessary for this specific expression.
Step-by-step explanation:
The phrase "decompose the fraction x² + x² + x - 42" suggests a misunderstanding or miscommunication regarding the terminology used. Decomposition often involves breaking down a fraction into simpler partial fractions or factoring an expression into its constituent parts. However, the given expression x² + x² + x - 42 doesn't represent a fraction; it's a polynomial expression.
If the objective were to factor the polynomial expression x² + x² + x - 42, it can be approached by combining like terms first. Grouping the terms with similar powers of x, the expression can be rewritten as 2x² + x - 42. Then, attempting to factor this quadratic expression by finding two numbers whose product is equal to the product of the quadratic term coefficient and the constant term (2 * -42 = -84) and whose sum is equal to the coefficient of the linear term (1), might be one approach. However, it's important to note that this expression may not factorize nicely with integer coefficients.
As the expression doesn't represent a fraction and the decomposition process commonly associated with fractions doesn't apply here straightforwardly, there might be a misunderstanding in the wording or the intended expression to be decomposed. The given expression might be rephrased or re-evaluated to reflect the correct mathematical operation intended for decomposition.