𝑓
परिमेय व्यंजक कैलकुलेटर
Simplify · Add · Subtract · Multiply · Divide · Evaluate · Domain Restrictions
Enter polynomial अंशs and हरs using standard notation (e.g. x^2-4, x+2). Get step-by-step factoring, cancellation, and the simplified result.
Simplify a Rational Expression
Factor & CancelQuick examples
Input notation guide
x^2 → x²
2x^2+3x-5 → 2x² + 3x − 5
x^2-9 → x² − 9 (difference of squares)
x^3-1 → x³ − 1 (difference of cubes)
4 → constant polynomial
x → linear monomial
-x+1 → −x + 1 (leading negative OK)
2x^2+3x-5 → 2x² + 3x − 5
x^2-9 → x² − 9 (difference of squares)
x^3-1 → x³ − 1 (difference of cubes)
4 → constant polynomial
x → linear monomial
-x+1 → −x + 1 (leading negative OK)
परिमेय व्यंजक क्या हैं?
परिमेय व्यंजक दो बहुपदों का अनुपात (fraction) होते हैं। इन्हें सरल करने के लिए अंश और हर के गुणनखंड किए जाते हैं।
अक्सर पूछे जाने वाले प्रश्न
What is a rational expression?
A rational expression is a fraction where both the अंश and हर are polynomials. Examples include (x+3)/(x-2) and (x²-1)/(x²+5x+6). They are undefined wherever the हर equals zero.
How do you simplify a rational expression?
Factor the अंश, factor the हर, then cancel any common factors. Always record domain restrictions — excluded values from the original हर apply even after cancellation.
Why must we exclude values from the domain?
Division by zero is undefined in mathematics. Any x that makes the हर zero must be excluded from the domain. Even after simplification these restrictions carry over from the original unsimplified form.
How do you find the LCD of polynomial हरs?
Factor each हर completely. Build the LCD by taking each unique factor to its highest power across all हरs. For example, x/(x-1) + 2/(x²-1): since x²-1 = (x-1)(x+1), the LCD = (x-1)(x+1).
What is the difference between domain and range?
The domain is the set of x-values for which the expression is defined (excludes हर zeros). The range is the set of all output values. Finding the range requires solving for x in terms of y and checking what y-values are achievable.
How do you add rational expressions?
Find the LCD, rewrite each fraction over the LCD by multiplying अंश and हर by the missing factors, combine अंशs into one fraction over the LCD, then simplify the result.
How do you divide rational expressions?
Multiply the first expression by the reciprocal (flip) of the second. Factor all pieces, cross-cancel common factors, then multiply. Note new restrictions from the divisor's अंश becoming a हर after flipping.
Does this calculator support x² and higher powers?
Yes. Enter polynomials using standard notation: x^2-4 for x²-4. The calculator factors quadratics and higher-degree polynomials, identifies common factors, and shows each cancellation step.