Algebra

Problems related to equations, functions, polynomials, etc.

Problems in this category

We need to solve the inequality $\frac{(x+2)|x-3|}{x^2+6} > -1$.

InequalitiesAbsolute ValueCase Analysis

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

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

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

The problem asks us to prove that the solution of the equation $\frac{3m}{9m^2 - 12mx + 4x^2} - \fra...

EquationsAlgebraic ManipulationRational Expressions

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

The problem asks to solve the equation $3v = h^2(3r - h)$ for $r$, where $v$ and $h$ are real number...

Equation SolvingVariable IsolationAlgebraic Manipulation

We need to solve the equation $\frac{x-1}{a-3} - \frac{ax}{a^2+3a+9} = \frac{21x-a^2}{a^3-27}$ for $...

EquationsAlgebraic ManipulationFactoringSolving for x

We are given the following equation and asked to solve for $x$: $$ \frac{3}{x-m} - \frac{2}{x+m} = \...

EquationsRational ExpressionsSolving Equations

Solve the equation $(2x - 3b)^2 = (x + 6b)(x - 9b)(8x - 12b) - (3b)^3$ for $x$.

Cubic EquationsPolynomial EquationsVariable Substitution

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