v) (a+4)/(a^(2)+3a-4)

Factor Denominator: Factor the denominator a^2 + 3a - 4. To factor the quadratic expression, we need to find two numbers that multiply to give -4 (the constant term) and add to give 3 (the coefficient of the middle term). The numbers that satisfy these conditions are 4 and -1. Therefore, we can write the denominator as (a + 4)(a - 1).Write Expression: Write the original expression with the factored denominator. The expression becomes (a + 4) / ((a + 4)(a - 1)).Cancel Common Factors: Cancel out the common factors in the numerator and the denominator. The term (a + 4) is common to both the numerator and the denominator, so we can cancel it out. The expression simplifies to 1 / (a - 1).

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v) $\frac{a+4}{a^{2}+3 a-4}$

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Algebra 1

Evaluate integers raised to rational exponents

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Q. v)

\frac{a+4}{a^{2}+3 a-4}

Factor Denominator: Factor the denominator $a^2 + 3a - 4$ . To factor the quadratic expression, we need to find two numbers that multiply to give $-4$ (the constant term) and add to give $3$ (the coefficient of the middle term). The numbers that satisfy these conditions are $4$ and $-1$ . Therefore, we can write the denominator as $(a + 4)(a - 1)$ .
Write Expression: Write the original expression with the factored denominator. $\newline$ The expression becomes $(a + 4) / ((a + 4)(a - 1))$ .
Cancel Common Factors: Cancel out the common factors in the numerator and the denominator. $\newline$ The term $(a + 4)$ is common to both the numerator and the denominator, so we can cancel it out. $\newline$ The expression simplifies to $\frac{1}{(a - 1)}$ .