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Fraction cross multiplication Calculator

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1

Solved example of fraction cross multiplication

$\frac{3x+1}{5x+7}=\frac{6x+11}{10x-3}$
2

Apply fraction cross-multiplication

$\left(3x+1\right)\left(10x-3\right)=\left(5x+7\right)\left(6x+11\right)$
3

Multiplying polynomials $3x+1$ and $10x-3$

$10x\left(3x+1\right)-3\left(3x+1\right)=\left(5x+7\right)\left(6x+11\right)$
4

Solve the product $10x\left(3x+1\right)$

$x\left(30x+10\right)-3\left(3x+1\right)=\left(5x+7\right)\left(6x+11\right)$
5

Solve the product $x\left(30x+10\right)$

$30x^2+10x-3\left(3x+1\right)=\left(5x+7\right)\left(6x+11\right)$
6

Solve the product $-3\left(3x+1\right)$

$30x^2+10x-9x-3=\left(5x+7\right)\left(6x+11\right)$
7

Multiplying polynomials $5x+7$ and $6x+11$

$30x^2+10x-9x-3=6x\left(5x+7\right)+11\left(5x+7\right)$
8

Solve the product $6x\left(5x+7\right)$

$30x^2+10x-9x-3=x\left(30x+42\right)+11\left(5x+7\right)$
9

Solve the product $x\left(30x+42\right)$

$30x^2+10x-9x-3=30x^2+42x+11\left(5x+7\right)$
10

Solve the product $11\left(5x+7\right)$

$30x^2+10x-9x-3=30x^2+42x+55x+77$
11

Grouping terms

$30x^2+10x-9x-3-\left(30x^2+42x+55x\right)=77$
12

Adding $10x$ and $-9x$

$x+30x^2-3-\left(30x^2+42x+55x\right)=77$
13

Solve the product $-\left(30x^2+42x+55x\right)$

$x+30x^2-3-30x^2-\left(42x+55x\right)=77$
14

Adding $30x^2$ and $-30x^2$

$0x^2+x-3-\left(42x+55x\right)=77$
15

Any expression multiplied by $0$ is equal to $0$

$-3+x-\left(42x+55x\right)=77$
16

Adding $42x$ and $55x$

$-3+x-97x=77$
17

Adding $-97x$ and $x$

$-96x-3=77$
18

Subtract $-3$ from both sides of the equation

$-96x=80$
19

Divide both sides of the equation by $-96$

$x=-\frac{5}{6}$

Answer

$x=-\frac{5}{6}$

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