Solve (4)/(sqrt(7)+3)

Question

ScanSolve AI Tutor · Accepted Answer

To rationalize the denominator of the expression $\frac{4}{\sqrt{7} + \sqrt{3}}$ , multiply the numerator and denominator by the conjugate of the denominator. The conjugate of $\sqrt{7} + \sqrt{3}$ is $\sqrt{7} - \sqrt{3}$ .

Multiply the fraction by $\frac{\sqrt{7} - \sqrt{3}}{\sqrt{7} - \sqrt{3}}$ .
$\frac{4}{\sqrt{7} + \sqrt{3}} \times \frac{\sqrt{7} - \sqrt{3}}{\sqrt{7} - \sqrt{3}}$
Expand the numerator.
$4(\sqrt{7} - \sqrt{3}) = 4\sqrt{7} - 4\sqrt{3}$
Expand the denominator using the difference of squares formula $(a+b)(a-b) = a^2 - b^2$ .
Here, $a = \sqrt{7}$ and $b = \sqrt{3}$ .
$(\sqrt{7} + \sqrt{3})(\sqrt{7} - \sqrt{3}) = (\sqrt{7})^2 - (\sqrt{3})^2$ $= 7 - 3$ $= 4$
Combine the simplified numerator and denominator.
$\frac{4\sqrt{7} - 4\sqrt{3}}{4}$
Simplify the fraction by dividing the numerator by the denominator.
$\frac{4(\sqrt{7} - \sqrt{3})}{4} = \sqrt{7} - \sqrt{3}$

Solve (4)/(sqrt(7)+3)

Answer

Step-by-step solution

Multiply the fraction by $\frac{\sqrt{7} - \sqrt{3}}{\sqrt{7} - \sqrt{3}}$ .

Expand the numerator.

Expand the denominator using the difference of squares formula $(a+b)(a-b) = a^2 - b^2$ .

Combine the simplified numerator and denominator.

Simplify the fraction by dividing the numerator by the denominator.

Try one yourself

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Solve (4)/(sqrt(7)+3)

Answer

Step-by-step solution

Multiply the fraction by 7−37−3\frac{\sqrt{7} - \sqrt{3}}{\sqrt{7} - \sqrt{3}}7​−3​7​−3​​.

Expand the numerator.

Expand the denominator using the difference of squares formula (a+b)(a−b)=a2−b2(a+b)(a-b) = a^2 - b^2(a+b)(a−b)=a2−b2.

Combine the simplified numerator and denominator.

Simplify the fraction by dividing the numerator by the denominator.

Try one yourself

Still stuck on this one?

More Mathematics Questions

Multiply the fraction by $\frac{\sqrt{7} - \sqrt{3}}{\sqrt{7} - \sqrt{3}}$ .

Expand the denominator using the difference of squares formula $(a+b)(a-b) = a^2 - b^2$ .