Algebra
Problems related to equations, functions, polynomials, etc.
Problems in this category
We are given the equation: $\frac{1}{(x-a-b)(x+a+b)} + \frac{1}{x^2 + a^2 + b^2 - 2ax - 2bx + 2ab} =...
Equation VerificationAlgebraic ManipulationRational Expressions
2025/5/25
We are given the equation: $\frac{1}{(x-a-b)(x+a+b)} + \frac{1}{x^2+a^2+b^2-2ax-2bx+2ab} = \frac{2}{...
Equation VerificationAlgebraic ManipulationFractionsError Analysis
2025/5/25
We are given the equation: $\frac{1}{(x-a-b)(x+a+b)} + \frac{1}{x^2 + a^2 + b^2 - 2ax - 2bx + 2ab} =...
Algebraic EquationsEquation VerificationSimplificationExpansion
2025/5/25
The problem is to solve the inequality $\frac{(x+1)|x-2|}{x^2+2} < -1$.
InequalitiesAbsolute ValueQuadratic InequalitiesCase Analysis
2025/5/25
We need to solve the inequality $\frac{(x+2)|x-3|}{x^2+6} > -1$.
InequalitiesAbsolute ValueCase Analysis
2025/5/25
The problem is to solve the equation for $x$, where $a$, $b$, and $c$ are real numbers: $\frac{a}{c}...
EquationsAlgebraic ManipulationRational ExpressionsVariable SolvingReal Numbers
2025/5/25
Solve the equation $\frac{2mx(m+1)+3x}{m^3-27} - \frac{x}{m-3} + \frac{x+1}{m^2+3m+9} = 0$ for $x$.
Algebraic EquationsRational ExpressionsSolving EquationsFactorizationDifference of Cubes
2025/5/25
The problem gives an equation $\frac{2x}{a^3 - 8} - \frac{a}{a^2 + 2a + 4} = \frac{x-1}{a-2}$, where...
EquationsSolving EquationsRational ExpressionsInequalitiesFactoring
2025/5/25
The problem asks us to prove that the solution of the equation $\frac{3m}{9m^2 - 12mx + 4x^2} - \fra...
EquationsAlgebraic ManipulationRational Expressions
2025/5/25
The problem is to solve the equation $M = \frac{n(v+w)}{v-w}$ for $v$. $M$, $n$, and $w$ are real nu...
Equation SolvingAlgebraic ManipulationLinear EquationsVariable Isolation
2025/5/25