Solve 4x+7/x-1=12x+5/3x+4

$$\frac { 4 x + 7 } { x - 1 } = \frac { 12 x + 5 } { 3 x + 4 }$$

Solve for x

$$x=-\frac{3}{4}=-0.75$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -\frac{4}{3},1 since division by zero is not defined. Multiply both sides of the equation by \left(x-1\right)\left(3x+4\right), the least common multiple of x-1,3x+4.

$$\left(3x+4\right)\left(4x+7\right)=\left(x-1\right)\left(12x+5\right)$$

Use the distributive property to multiply 3x+4 by 4x+7 and combine like terms.

$$12x^{2}+37x+28=\left(x-1\right)\left(12x+5\right)$$

Use the distributive property to multiply x-1 by 12x+5 and combine like terms.

$$12x^{2}+37x+28=12x^{2}-7x-5$$

Subtract 12x^{2} from both sides.

$$12x^{2}+37x+28-12x^{2}=-7x-5$$

Combine 12x^{2} and -12x^{2} to get 0.

$$37x+28=-7x-5$$

Add 7x to both sides.

$$37x+28+7x=-5$$

Combine 37x and 7x to get 44x.

$$44x+28=-5$$

Subtract 28 from both sides.

$$44x=-5-28$$

Subtract 28 from -5 to get -33.

$$44x=-33$$

Divide both sides by 44.

$$x=\frac{-33}{44}$$

Reduce the fraction \frac{-33}{44} to lowest terms by extracting and canceling out 11.

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