Solve 4x+6/3(x-1)-5x-4/x-1=1

$$\frac { 4 x + 6 } { 3 ( x - 1 ) } - \frac { 5 x - 4 } { x - 1 } = 1$$

Solve for x

$$x = \frac{3}{2} = 1\frac{1}{2} = 1.5$$

Steps for Solving Linear Equation

Variable x cannot be equal to 1 since division by zero is not defined. Multiply both sides of the equation by 3\left(x-1\right), the least common multiple of 3\left(x-1\right),x-1.

$$4x+6-3\left(5x-4\right)=3\left(x-1\right)$$

Use the distributive property to multiply -3 by 5x-4.

$$4x+6-15x+12=3\left(x-1\right)$$

Combine 4x and -15x to get -11x.

$$-11x+6+12=3\left(x-1\right)$$

Add 6 and 12 to get 18.

$$-11x+18=3\left(x-1\right)$$

Use the distributive property to multiply 3 by x-1.

$$-11x+18=3x-3$$

Subtract 3x from both sides.

$$-11x+18-3x=-3$$

Combine -11x and -3x to get -14x.

$$-14x+18=-3$$

Subtract 18 from both sides.

$$-14x=-3-18$$

Subtract 18 from -3 to get -21.

$$-14x=-21$$

Divide both sides by -14.

$$x=\frac{-21}{-14}$$

Reduce the fraction \frac{-21}{-14} to lowest terms by extracting and canceling out -7.

$$x=\frac{3}{2}$$