Solve (2a-1)=a+7/a+1

$$( 2 a - 1 ) = \frac { a + 7 } { a + 1 }$$

Solve for a

$$a=-2$$

$$a=2$$

Steps by Finding Square Root

Variable a cannot be equal to -1 since division by zero is not defined. Multiply both sides of the equation by a+1.

$$2a\left(a+1\right)+\left(a+1\right)\left(-1\right)=a+7$$

Use the distributive property to multiply 2a by a+1.

$$2a^{2}+2a+\left(a+1\right)\left(-1\right)=a+7$$

Use the distributive property to multiply a+1 by -1.

$$2a^{2}+2a-a-1=a+7$$

Combine 2a and -a to get a.

$$2a^{2}+a-1=a+7$$

Subtract a from both sides.

$$2a^{2}+a-1-a=7$$

Combine a and -a to get 0.

$$2a^{2}-1=7$$

Add 1 to both sides.

$$2a^{2}=7+1$$

Add 7 and 1 to get 8.

$$2a^{2}=8$$

Divide both sides by 2.

$$a^{2}=\frac{8}{2}$$

Divide 8 by 2 to get 4.

$$a^{2}=4$$

Take the square root of both sides of the equation.

$$a=2 a=-2$$

Steps Using the Quadratic Formula

Variable a cannot be equal to -1 since division by zero is not defined. Multiply both sides of the equation by a+1.

$$2a\left(a+1\right)+\left(a+1\right)\left(-1\right)=a+7$$

Use the distributive property to multiply 2a by a+1.

$$2a^{2}+2a+\left(a+1\right)\left(-1\right)=a+7$$

Use the distributive property to multiply a+1 by -1.

$$2a^{2}+2a-a-1=a+7$$

Combine 2a and -a to get a.

$$2a^{2}+a-1=a+7$$

Subtract a from both sides.

$$2a^{2}+a-1-a=7$$

Combine a and -a to get 0.

$$2a^{2}-1=7$$

Subtract 7 from both sides.

$$2a^{2}-1-7=0$$

Subtract 7 from -1 to get -8.

$$2a^{2}-8=0$$

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

$$a=\frac{0±\sqrt{0^{2}-4\times 2\left(-8\right)}}{2\times 2}$$

Square 0.

$$a=\frac{0±\sqrt{-4\times 2\left(-8\right)}}{2\times 2}$$

Multiply -4 times 2.

$$a=\frac{0±\sqrt{-8\left(-8\right)}}{2\times 2}$$

Multiply -8 times -8.

$$a=\frac{0±\sqrt{64}}{2\times 2}$$

Take the square root of 64.

$$a=\frac{0±8}{2\times 2}$$

Multiply 2 times 2.

$$a=\frac{0±8}{4}$$

Now solve the equation a=\frac{0±8}{4} when ± is plus. Divide 8 by 4.

$$a=2$$

Now solve the equation a=\frac{0±8}{4} when ± is minus. Divide -8 by 4.

$$a=-2$$

The equation is now solved.

$$a=2 a=-2$$