Simplifying rational expressions is a part of syllabus in algebra 1 (second math course), Simplify expressions means factorising numerator and denominator and cancelling the common factors. Adding and subtracting rational expressions involve finding the LCD (Lowest Common Denominator) and rewrite each expression with this and then add/subtract the numerators. For, multiplying and dividing rational expressions, factorise the numerators and denominators and cancel the common factors. Rational equations are equations with rational expressions of a variable. Learn more about rational expressions using the resources on this page.
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Once the numerator and the denominator have been factored, cross out any common factors. Factor the numerator: 6x 2 -21x – 12 = 3(2x 2 – 7x – 4) = 3(x – 4)(2x + 1) . Factor the denominator: 54x 2 +45x + 9 = 9(6x 2 + 5x + 1) = 9(3x + 1)(2x + 1) . Factor the numerator: x 3 – x = x(x 2 – 1) = x(x + 1)(x – 1) .
In mathematics, a rational function is any function which can be defined by a rational fraction, i.e. an algebraic fraction such that both the numerator and the denominator are polynomials. The coefficients of the polynomials need not be rational numbers, they may be taken in any field K.
f(x)=4×3 + √x − 1 is not a polynomial as it contains a square root. And f(x)=5×4 − 2×2 + 3/x is not a polynomial as it contains a ‘divide by x’. A polynomial is a function of the form f(x) = anxn + an−1xn−1 + … + a2x2 + a1x + a0 . The degree of a polynomial is the highest power of x in its expression.
A rational equation is an equation in which one or more of the terms is a fractional one. When solving these rational equations, we utilize one of two methods that will eliminate the denominator of each of the terms.
