Solve (5x-7)/(x-3)=(4x-3)/(x) | Equatix - Math Solver

Fractions & Decimals

Ratios & Proportions

Basic Number Theory

Integers & Absolute Values

Factors & Multiples

Prime Factorization

Basic Equations & Inequalities

Coordinate Plane & Graphing

Linear Equations & Inequalities

Quadratic Equations

Polynomials & Factoring

Functions & Graphs

Systems of Equations

Trigonometric Functions

Trigonometric Identities & Equations

Right Triangle Trigonometry

Graphing Trigonometric Functions

Limits & Continuity

Derivatives & Applications

Integrals & Applications

Series & Sequences

Multivariable Calculus

Functions & Graphs

Polynomial & Rational Functions

Exponential & Logarithmic Functions

Sequences & Series

Descriptive Statistics

Normal Distribution

Hypothesis Testing

Regression Analysis

Linear Programming

Sets & Counting

Eigenvalues & Eigenvectors

Linear Transformations

Atomic Structure

Thermochemistry

Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$\frac{ 5x-7 }{ x-3 } = \frac{ 4x-3 }{ x }$$

Solve for x

$x=-9$
$x=1$

Steps Using the Quadratic Formula

Steps for Completing the Square

Steps Using the Quadratic Formula

Variable $x$ cannot be equal to any of the values $0,3$ since division by zero is not defined. Multiply both sides of the equation by $x\left(x-3\right)$, the least common multiple of $x-3,x$.

$$x\left(5x-7\right)=\left(x-3\right)\left(4x-3\right)$$

Use the distributive property to multiply $x$ by $5x-7$.

$$5x^{2}-7x=\left(x-3\right)\left(4x-3\right)$$

Use the distributive property to multiply $x-3$ by $4x-3$ and combine like terms.

$$5x^{2}-7x=4x^{2}-15x+9$$

Subtract $4x^{2}$ from both sides.

$$5x^{2}-7x-4x^{2}=-15x+9$$

Combine $5x^{2}$ and $-4x^{2}$ to get $x^{2}$.

$$x^{2}-7x=-15x+9$$

Add $15x$ to both sides.

$$x^{2}-7x+15x=9$$

Combine $-7x$ and $15x$ to get $8x$.

$$x^{2}+8x=9$$

Subtract $9$ from both sides.

$$x^{2}+8x-9=0$$

This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $1$ for $a$, $8$ for $b$, and $-9$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.

$$x=\frac{-8±\sqrt{8^{2}-4\left(-9\right)}}{2}$$

Square $8$.

$$x=\frac{-8±\sqrt{64-4\left(-9\right)}}{2}$$

Multiply $-4$ times $-9$.

$$x=\frac{-8±\sqrt{64+36}}{2}$$

Add $64$ to $36$.

$$x=\frac{-8±\sqrt{100}}{2}$$

Take the square root of $100$.

$$x=\frac{-8±10}{2}$$

Now solve the equation $x=\frac{-8±10}{2}$ when $±$ is plus. Add $-8$ to $10$.

$$x=\frac{2}{2}$$

Divide $2$ by $2$.

$$x=1$$

Now solve the equation $x=\frac{-8±10}{2}$ when $±$ is minus. Subtract $10$ from $-8$.

$$x=-\frac{18}{2}$$

Divide $-18$ by $2$.

$$x=-9$$

The equation is now solved.

$$x=1$$ $$x=-9$$

Steps for Completing the Square

Variable $x$ cannot be equal to any of the values $0,3$ since division by zero is not defined. Multiply both sides of the equation by $x\left(x-3\right)$, the least common multiple of $x-3,x$.

$$x\left(5x-7\right)=\left(x-3\right)\left(4x-3\right)$$

Use the distributive property to multiply $x$ by $5x-7$.

$$5x^{2}-7x=\left(x-3\right)\left(4x-3\right)$$

Use the distributive property to multiply $x-3$ by $4x-3$ and combine like terms.

$$5x^{2}-7x=4x^{2}-15x+9$$

Subtract $4x^{2}$ from both sides.

$$5x^{2}-7x-4x^{2}=-15x+9$$

Combine $5x^{2}$ and $-4x^{2}$ to get $x^{2}$.

$$x^{2}-7x=-15x+9$$

Add $15x$ to both sides.

$$x^{2}-7x+15x=9$$

Combine $-7x$ and $15x$ to get $8x$.

$$x^{2}+8x=9$$

Divide $8$, the coefficient of the $x$ term, by $2$ to get $4$. Then add the square of $4$ to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+8x+4^{2}=9+4^{2}$$

Square $4$.

$$x^{2}+8x+16=9+16$$

Add $9$ to $16$.

$$x^{2}+8x+16=25$$

Factor $x^{2}+8x+16$. In general, when $x^{2}+bx+c$ is a perfect square, it can always be factored as $\left(x+\frac{b}{2}\right)^{2}$.

$$\left(x+4\right)^{2}=25$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+4\right)^{2}}=\sqrt{25}$$

Simplify.

$$x+4=5$$ $$x+4=-5$$

Subtract $4$ from both sides of the equation.

$$x=1$$ $$x=-9$$