Algebra
Problems related to equations, functions, polynomials, etc.
Problems in this category
The problem asks to find the range of the function $g(x) = x^2 + 9$ for the domain $\{-2, -1, 0, 1, ...
FunctionsRangeQuadratic FunctionsEvaluation
2025/4/21
The problem asks us to find the domain of the function $d(x) = 4 - \frac{1}{5}x$ for the range $\{0,...
FunctionsLinear FunctionsDomain and Range
2025/4/21
The problem asks to find the least common denominator (LCD) of the two rational expressions: $\frac{...
Rational ExpressionsLeast Common Denominator (LCD)PolynomialsAlgebraic FractionsExponents
2025/4/21
We are asked to simplify the complex fraction $\frac{c^2 + 7c + 10}{\frac{c^2 + 5c}{c^3 + 2c^2}}$.
PolynomialsSimplificationFactoringRational Expressions
2025/4/21
We are given the quadratic equation $2x(x-1) + 9 = 7$ and asked to determine the nature of its solut...
Quadratic EquationsDiscriminantComplex NumbersRoots of Equations
2025/4/21
The problem asks us to determine the type of solutions the quadratic equation $2x^2 + 18 = -12x$ has...
Quadratic EquationsDiscriminantReal RootsRational Roots
2025/4/21
We are asked to determine the type of solutions the quadratic equation $9x^2 + 14x + 5 = 0$ has by u...
Quadratic EquationsDiscriminantRoots of EquationsReal SolutionsRational Solutions
2025/4/21
The problem is to solve the equation $\frac{1}{12} + \frac{1}{y} = \frac{3}{y+6}$ for $y$ using the ...
Quadratic EquationsEquation SolvingRational EquationsQuadratic Formula
2025/4/21
We are asked to simplify the compound fraction $\frac{\frac{x-7}{x+2}}{\frac{x^2-49}{5x+10}}$.
Algebraic SimplificationRational ExpressionsFactorizationDifference of Squares
2025/4/21
The problem requires us to simplify the equation $(x-2)(x+1) = \frac{2x+19}{2}$ and then solve for $...
Quadratic EquationsQuadratic FormulaEquation SolvingSimplification
2025/4/21